Andrew Knyazev

Andrew Knyazev
  • Phone: 617-621-7516
  • Email: knyazev[at]merl[dot]com
  • Position:
    Research / Technical Staff

    Distinguished Member Research Staff
  • Education:
    Ph.D., Inst of Numerical Math, Soviet Acad of Sciences, 1985
  • Research Area:
  • External Links:
  • Biography

    During his 30 years in the academy, Andrew contributed to numerical analysis of partial differential equations and computational linear algebra, with emphasis on eigenvalue problems.  His focus at MERL is on novel algorithms for image & video processing, data analytics, data transmission, and model predictive control.

  • News & Events

    •  TALK   Anomaly Detection in Very Large Graphs: Modeling and Computational Considerations
      Date & Time: Thursday, May 2, 2013; 12:00 PM
      Speaker: Ben Miller, MIT
      MERL Host: Andrew Knyazev
      Research Area: Algorithms
      Brief
      • Graph theory provides an intuitive mathematical foundation for dealing with relational data, but there are numerous computational challenges in the detection of interesting behavior within small subsets of vertices, especially as the graphs grow larger and the behavior becomes more subtle. This presentation discusses computational considerations of a residuals-based subgraph detection framework, including the implications on inference with recent statistical models. We also present scaling properties, demonstrating analysis of a billion-vertex graph using commodity hardware.
    •  
    •  NEWS   SIAM Journal of Scientific Computing: publication by Andrew Knyazev and others
      Date: March 14, 2013
      Where: SIAM Journal of Scientific Computing
      MERL Contact: Andrew Knyazev
      Research Areas: Algorithms
      Brief
      • The article "Absolute Value Preconditioning for Symmetric Indefinite Linear Systems" by Vecharynski, E. and Knyazev, A.V. was published in SIAM Journal of Scientific Computing
    •  

    See All News & Events for Andrew
  • MERL Publications

    •  Zhu, P., Knyazev, A.F., "Angles Between Subspaces and Their Tangents", Journal of Numerical Mathematics, November 2013.
    •  Bouwmeester, H., Dougherty, A., Knyazev, A.V., "Nonsymmetric Multigrid Preconditioning for Conjugate Gradient Methods", arXiv, Computer Science, Numerical Analysis, June 2013.
      BibTeX Download PDFRead TR2013-027
      • @techreport{MERL_TR2013-027,
      • author = {Bouwmeester, H. and Dougherty, A. and Knyazev, A.V.},
      • title = {Nonsymmetric Multigrid Preconditioning for Conjugate Gradient Methods},
      • institution = {MERL - Mitsubishi Electric Research Laboratories},
      • address = {201 Broadway, Cambridge, MA 02139},
      • number = {TR2013-027},
      • month = jun,
      • year = 2013
      • url = {http://www.merl.com/publications/TR2013-027/}
      • }
    •  Zhu, P., Argentati, M.E., Knyazev, A.V., "Bounds for the Rayleigh Quotient and the Spectrum of Self-Adjoint Operators", SIAM Journal on Matrix Analysis and Applications, March 2013.
      BibTeX Download PDFRead TR2013-068
      • @article{Zhu2013mar,
      • author = {Zhu, P. and Argentati, M.E. and Knyazev, A.V.},
      • title = {Bounds for the Rayleigh Quotient and the Spectrum of Self-Adjoint Operators},
      • journal = {SIAM Journal on Matrix Analysis and Applications},
      • year = 2013,
      • month = mar,
      • url = {http://www.merl.com/publications/TR2013-068}
      • }
    •  Vecharynski, E., Knyazev, A.V., "Absolute Value Preconditioning for Symmetric Indefinite Linear Systems", SIAM Journal of Scientific Computing, DOI: 10.1137/120886686, Vol. 35(2), pp. A696-A718, March 2013.
      BibTeX Download PDFRead TR2013-016
      • @article{Vecharynski2013mar,
      • author = {Vecharynski, E. and Knyazev, A.V.},
      • title = {Absolute Value Preconditioning for Symmetric Indefinite Linear Systems},
      • journal = {SIAM Journal of Scientific Computing},
      • year = 2013,
      • volume = {35(2)},
      • pages = {A696--A718},
      • month = mar,
      • doi = {10.1137/120886686},
      • url = {http://www.merl.com/publications/TR2013-016}
      • }
    •  Knyazev, A.V., Zhu, P., "Principal angles between subspaces and their tangents", arXiv, September 2012.
      BibTeX Download PDFRead TR2012-058
      • @inproceedings{Zhu2012sep,
      • author = {Zhu, P. and Knyazev, A.},
      • title = {Principal angles between subspaces and their tangents},
      • booktitle = {arXiv},
      • year = 2012,
      • month = sep,
      • url = {http://www.merl.com/publications/TR2012-058}
      • }
  • Other Publications

    •  E. Vecharynski and A. Knyazev, "Absolute Value Preconditioning for Symmetric Indefinite Linear Systems", SIAM Journal on Scientific Computing, Vol. 35, No. 2, pp. A696-A718, 2013.
      BibTeX
      • @Article{Vecharynski2013,
      • author = {Vecharynski, E. and Knyazev, A.},
      • title = {Absolute Value Preconditioning for Symmetric Indefinite Linear Systems},
      • journal = {SIAM Journal on Scientific Computing},
      • year = 2013,
      • volume = 35,
      • number = 2,
      • pages = {A696--A718},
      • url = {http://epubs.siam.org/doi/abs/10.1137/120886686}
      • }
    •  P. Zhu, M. Argentati and A. Knyazev, "Bounds for the Rayleigh Quotient and the Spectrum of Self-Adjoint Operators", SIAM Journal on Matrix Analysis and Applications, Vol. 34, No. 1, pp. 244-256, 2013.
      BibTeX
      • @Article{Zhu2013,
      • author = {Zhu, P. and Argentati, M. and Knyazev, A.},
      • title = {Bounds for the Rayleigh Quotient and the Spectrum of Self-Adjoint Operators},
      • journal = {SIAM Journal on Matrix Analysis and Applications},
      • year = 2013,
      • volume = 34,
      • number = 1,
      • pages = {244--256},
      • url = {http://epubs.siam.org/doi/abs/10.1137/120884468}
      • }
    •  A. Knyazev, A. Jujunashvili and M. Argentati, "Angles between infinite dimensional subspaces with applications to the Rayleigh-Ritz and alternating projectors methods", Journal of Functional Analysis, Times Cited: 1 Knyazev, Andrew Jujunashvili, Abram Argentati, Merico, Vol. 259, No. 6, pp. 1323-1345, 2010.
      BibTeX
      • @Article{Knyazev2010,
      • author = {Knyazev, A. and Jujunashvili, A. and Argentati, M.},
      • title = {Angles between infinite dimensional subspaces with applications to the Rayleigh-Ritz and alternating projectors methods},
      • journal = {Journal of Functional Analysis},
      • year = 2010,
      • volume = 259,
      • number = 6,
      • pages = {1323--1345},
      • note = {Times Cited: 1 Knyazev, Andrew Jujunashvili, Abram Argentati, Merico}
      • }
    •  A. V. Knyazev and M. E. Argentati, "Rayleigh-ritz Majorization Error Bounds With Applications To Fem", Siam Journal on Matrix Analysis and Applications, Times Cited: 2 Knyazev, Andrew V. Argentati, Merico E., Vol. 31, No. 3, pp. 1521-1537, 2010.
      BibTeX
      • @Article{Knyazev2010a,
      • author = {Knyazev, A. V. and Argentati, M. E.},
      • title = {Rayleigh-ritz Majorization Error Bounds With Applications To Fem},
      • journal = {Siam Journal on Matrix Analysis and Applications},
      • year = 2010,
      • volume = 31,
      • number = 3,
      • pages = {1521--1537},
      • note = {Times Cited: 2 Knyazev, Andrew V. Argentati, Merico E.}
      • }
    •  A. V. Knyazev and K. Neymeyr, "Gradient Flow Approach To Geometric Convergence Analysis Of Preconditioned Eigensolvers", Siam Journal on Matrix Analysis and Applications, Times Cited: 3 Knyazev, Andrew V. Neymeyr, Klaus, Vol. 31, No. 2, pp. 621-628, 2009.
      BibTeX
      • @Article{Knyazev2009,
      • author = {Knyazev, A. V. and Neymeyr, K.},
      • title = {Gradient Flow Approach To Geometric Convergence Analysis Of Preconditioned Eigensolvers},
      • journal = {Siam Journal on Matrix Analysis and Applications},
      • year = 2009,
      • volume = 31,
      • number = 2,
      • pages = {621--628},
      • note = {Times Cited: 3 Knyazev, Andrew V. Neymeyr, Klaus}
      • }
    •  M. E. Argentati, A. V. Knyazev, C. C. Paige and I. Panayotov, "Bounds On Changes In Ritz Values For A Perturbed Invariant Subspace Of A Hermitian Matrix", Siam Journal on Matrix Analysis and Applications, Vol. 30, No. 2, pp. 548-559, 2008.
      BibTeX
      • @Article{Argentati2008,
      • author = {Argentati, M. E. and Knyazev, A. V. and Paige, C. C. and Panayotov, I.},
      • title = {Bounds On Changes In Ritz Values For A Perturbed Invariant Subspace Of A Hermitian Matrix},
      • journal = {Siam Journal on Matrix Analysis and Applications},
      • year = 2008,
      • volume = 30,
      • number = 2,
      • pages = {548--559}
      • }
    •  F. Bottin, S. Leroux, A. Knyazev and G. Zerah, "Large-scale ab initio calculations based on three levels of parallelization", Computational Materials Science, Times Cited: 14 Bottin, Francois Leroux, Stephane Knyazev, Andrew Zerah, Gilles, Vol. 42, No. 2, pp. 329-336, 2008.
      BibTeX
      • @Article{Bottin2008,
      • author = {Bottin, F. and Leroux, S. and Knyazev, A. and Zerah, G.},
      • title = {Large-scale ab initio calculations based on three levels of parallelization},
      • journal = {Computational Materials Science},
      • year = 2008,
      • volume = 42,
      • number = 2,
      • pages = {329--336},
      • note = {Times Cited: 14 Bottin, Francois Leroux, Stephane Knyazev, Andrew Zerah, Gilles}
      • }
    •  A. V. Knyazev, "Observations on degenerate saddle point problems", Computer Methods in Applied Mechanics and Engineering, Times Cited: 0 Knyazev, Andrew V., Vol. 196, No. 37-40, pp. 3742-3749, 2007.
      BibTeX
      • @Article{Knyazev2007,
      • author = {Knyazev, A. V.},
      • title = {Observations on degenerate saddle point problems},
      • journal = {Computer Methods in Applied Mechanics and Engineering},
      • year = 2007,
      • volume = 196,
      • number = {37-40},
      • pages = {3742--3749},
      • note = {Times Cited: 0 Knyazev, Andrew V.}
      • }
    •  A. V. Knyazev, M. E. Argentati, I. Lashuk and E. E. Ovtchinnikov, "Block locally optimal preconditioned eigenvalue Xolvers (BLOPEX) in hypre and PETSc", Siam Journal on Scientific Computing, Vol. 29, No. 5, pp. 2224-2239, 2007.
      BibTeX
      • @Article{Knyazev2007a,
      • author = {Knyazev, A. V. and Argentati, M. E. and Lashuk, I. and Ovtchinnikov, E. E.},
      • title = {Block locally optimal preconditioned eigenvalue Xolvers (BLOPEX) in hypre and PETSc},
      • journal = {Siam Journal on Scientific Computing},
      • year = 2007,
      • volume = 29,
      • number = 5,
      • pages = {2224--2239}
      • }
    •  I. Lashuk, M.E. Argentati, Ovchinnikov E. and A.V. Knyazev, "Preconditioned Eigensolver LOBPCG in hypre and PETSc", 2007.
      BibTeX
      • @Misc{Lashuk2007,
      • author = {Lashuk, I. and Argentati, M.E. and E., Ovchinnikov and Knyazev, A.V.},
      • title = {Preconditioned Eigensolver LOBPCG in hypre and PETSc},
      • year = 2007,
      • volume = 55,
      • pages = {635--642},
      • publisher = {Springer}
      • }
    •  Z. J. Bai, A. Knyazev and H. A. van der Vorst, "Large scale linear and nonlinear eigenvalue problems - Preface", Linear Algebra and Its Applications, Times Cited: 0 Bai, ZJ Knyazev, A van der Vorst, HA, Vol. 415, No. 1, pp. 1-2, 2006.
      BibTeX
      • @Article{Bai2006,
      • author = {Bai, Z. J. and Knyazev, A. and van der Vorst, H. A.},
      • title = {Large scale linear and nonlinear eigenvalue problems - Preface},
      • journal = {Linear Algebra and Its Applications},
      • year = 2006,
      • volume = 415,
      • number = 1,
      • pages = {1--2},
      • note = {Times Cited: 0 Bai, ZJ Knyazev, A van der Vorst, HA}
      • }
    •  A. V. Knyazev and M. E. Argentati, "Majorization for changes in angles between subspaces, Ritz values, and graph Laplacian spectra", Siam Journal on Matrix Analysis and Applications, Times Cited: 6 Knyazev, Andrew V. Argentati, Merico E. 12th ILAS Conference JUN, 2005 CANADA, Vol. 29, No. 1, pp. 15-32, 2006.
      BibTeX
      • @Article{Knyazev2006,
      • author = {Knyazev, A. V. and Argentati, M. E.},
      • title = {Majorization for changes in angles between subspaces, Ritz values, and graph Laplacian spectra},
      • journal = {Siam Journal on Matrix Analysis and Applications},
      • year = 2006,
      • volume = 29,
      • number = 1,
      • pages = {15--32},
      • note = {Times Cited: 6 Knyazev, Andrew V. Argentati, Merico E. 12th ILAS Conference JUN, 2005 CANADA}
      • }
    •  A. V. Knyazev and M. E. Argentati, "On proximity of Rayleigh quotients for different vectors and Ritz values generated by different trial subspaces", Linear Algebra and Its Applications, Times Cited: 4 Knyazev, AV Argentati, ME, Vol. 415, No. 1, pp. 82-95, 2006.
      BibTeX
      • @Article{Knyazev2006a,
      • author = {Knyazev, A. V. and Argentati, M. E.},
      • title = {On proximity of Rayleigh quotients for different vectors and Ritz values generated by different trial subspaces},
      • journal = {Linear Algebra and Its Applications},
      • year = 2006,
      • volume = 415,
      • number = 1,
      • pages = {82--95},
      • note = {Times Cited: 4 Knyazev, AV Argentati, ME}
      • }
    •  A. V. Knyazev and I. Lashuk, "Steepest descent and conjugate gradient methods with variable preconditioning", Siam Journal on Matrix Analysis and Applications, Times Cited: 0 Knyazev, Andrew V. Lashuk, Ilya, Vol. 29, No. 4, pp. 1267-1280, 2006.
      BibTeX
      • @Article{Knyazev2006b,
      • author = {Knyazev, A. V. and Lashuk, I.},
      • title = {Steepest descent and conjugate gradient methods with variable preconditioning},
      • journal = {Siam Journal on Matrix Analysis and Applications},
      • year = 2006,
      • volume = 29,
      • number = 4,
      • pages = {1267--1280},
      • note = {Times Cited: 0 Knyazev, Andrew V. Lashuk, Ilya}
      • }
    •  A. V. Knyazev and J. E. Osborn, "New a priori fem error estimates for eigenvalues", Siam Journal on Numerical Analysis, Times Cited: 16 Knyazev, AV Osborn, JE, Vol. 43, No. 6, pp. 2647-2667, 2006.
      BibTeX
      • @Article{Knyazev2006c,
      • author = {Knyazev, A. V. and Osborn, J. E.},
      • title = {New a priori fem error estimates for eigenvalues},
      • journal = {Siam Journal on Numerical Analysis},
      • year = 2006,
      • volume = 43,
      • number = 6,
      • pages = {2647--2667},
      • note = {Times Cited: 16 Knyazev, AV Osborn, JE}
      • }
    •  S. Billups, A. Knyazev and J. Mandel, "6th IMACS International Symposium on Iterative Methods in Scientific Computing 27-30 March 2003, University of Colorado at Denver, Denver, Colorado, USA - Introduction", Applied Numerical Mathematics, Times Cited: 0 Billups, S Knyazev, A Mandel, J, Vol. 54, No. 2, pp. 105-106, 2005.
      BibTeX
      • @Article{Billups2005,
      • author = {Billups, S. and Knyazev, A. and Mandel, J.},
      • title = {6th IMACS International Symposium on Iterative Methods in Scientific Computing 27-30 March 2003, University of Colorado at Denver, Denver, Colorado, USA - Introduction},
      • journal = {Applied Numerical Mathematics},
      • year = 2005,
      • volume = 54,
      • number = 2,
      • pages = {105--106},
      • note = {Times Cited: 0 Billups, S Knyazev, A Mandel, J}
      • }
    •  J. Mandel, L. S. Bennethum, M. S. Chen, J. L. Coen, C. C. Douglas, L. P. Franca, C. J. Johns, M. J. Kim, A. V. Knyazev, R. Kremens, V. Kulkarni, G. Qin, A. Vodacek, J. J. Wu, W. Zhao and A. Zornes, "Towards a dynamic data driven application system for wildfire simulation", 2005, Computational Science - Iccs 2005, Pt 2.
      BibTeX
      • @Inbook{Mandel2005,
      • author = {Mandel, J. and Bennethum, L. S. and Chen, M. S. and Coen, J. L. and Douglas, C. C. and Franca, L. P. and Johns, C. J. and Kim, M. J. and Knyazev, A. V. and Kremens, R. and Kulkarni, V. and Qin, G. and Vodacek, A. and Wu, J. J. and Zhao, W. and Zornes, A.},
      • title = {Towards a dynamic data driven application system for wildfire simulation},
      • booktitle = {Computational Science - Iccs 2005, Pt 2},
      • year = 2005,
      • editor = {Sunderam, V. S. and VanAlbada, G. D. and Sloot, P. M. A. and Dongarra, J. J.},
      • volume = 3515,
      • series = {Lecture Notes in Computer Science},
      • pages = {632--639},
      • note = {Times Cited: 3 Mandel, J Bennethum, LS Chen, MS Coen, JL Douglas, CC Franca, LP Johns, CJ Kim, MJ Knyazev, AV Kremens, R Kulkarni, V Qin, G Vodacek, A Wu, JJ Zhao, W Zornes, A 5th International Conference on Computational Science (ICCS 2005) MAY 22-25, 2005 Atlanta, GA}
      • }
    •  A. V. Knyazev and K. Neymeyr, "A geometric theory for preconditioned inverse iteration III: A short and sharp convergence estimate for generalized eigenvalue problems", Linear Algebra and Its Applications, Times Cited: 31 Knyazev, AV Neymeyr, K 3rd International Workshop on Accurate Solution of Eigenvalue Problems JUL 03-06, 2002 HAGEN, GERMANY, Vol. 358, pp. 95-114, 2003.
      BibTeX
      • @Article{Knyazev2003,
      • author = {Knyazev, A. V. and Neymeyr, K.},
      • title = {A geometric theory for preconditioned inverse iteration III: A short and sharp convergence estimate for generalized eigenvalue problems},
      • journal = {Linear Algebra and Its Applications},
      • year = 2003,
      • volume = 358,
      • pages = {95--114},
      • note = {Times Cited: 31 Knyazev, AV Neymeyr, K 3rd International Workshop on Accurate Solution of Eigenvalue Problems JUL 03-06, 2002 HAGEN, GERMANY}
      • }
    •  A. Knyazev and O. Widlund, "Lavrentiev regularization plus Ritz approximation = uniform finite element error estimates for differential equations with rough coefficients", Mathematics of Computation, Times Cited: 9 Knyazev, A Widlund, O, Vol. 72, No. 241, pp. 17-40, 2003.
      BibTeX
      • @Article{Knyazev2003a,
      • author = {Knyazev, A. and Widlund, O.},
      • title = {Lavrentiev regularization plus Ritz approximation = uniform finite element error estimates for differential equations with rough coefficients},
      • journal = {Mathematics of Computation},
      • year = 2003,
      • volume = 72,
      • number = 241,
      • pages = {17--40},
      • note = {Times Cited: 9 Knyazev, A Widlund, O}
      • }
    •  Andrew V Knyazev, "Analysis of transmission problems on Lipschitz boundaries in stronger norms", Journal of Numerical Mathematics jnma, Vol. 11, No. 3, pp. 225-234, 2003.
      BibTeX
      • @Article{Knyazev2003b,
      • author = {Knyazev, Andrew V},
      • title = {Analysis of transmission problems on Lipschitz boundaries in stronger norms},
      • journal = {Journal of Numerical Mathematics jnma},
      • year = 2003,
      • volume = 11,
      • number = 3,
      • pages = {225--234}
      • }
    •  Andrew V. Knyazev and Klaus Neymeyr, "Efficient solution of symmetric eigenvalue problems using multigrid preconditioners in the locally optimal block conjugate gradient method.", Electronic Transactions on Numerical Analysis, Vol. 15, pp. 38-55, 2003.
      BibTeX
      • @Article{Knyazev2003c,
      • author = {Knyazev, Andrew V. and Neymeyr, Klaus},
      • title = {Efficient solution of symmetric eigenvalue problems using multigrid preconditioners in the locally optimal block conjugate gradient method.},
      • journal = {Electronic Transactions on Numerical Analysis},
      • year = 2003,
      • volume = 15,
      • pages = {38--55}
      • }
    •  N. S. Bakhvalov, A. V. Knyazev and R. R. Parashkevov, "Extension theorems for Stokes and Lame equations for nearly incompressible media and their applications to numerical solution of problems with highly discontinuous coefficients", Numerical Linear Algebra with Applications, Times Cited: 1 Bakhvalov, NS Knyazev, AV Parashkevov, RR, Vol. 9, No. 2, pp. 115-139, 2002.
      BibTeX
      • @Article{Bakhvalov2002,
      • author = {Bakhvalov, N. S. and Knyazev, A. V. and Parashkevov, R. R.},
      • title = {Extension theorems for Stokes and Lame equations for nearly incompressible media and their applications to numerical solution of problems with highly discontinuous coefficients},
      • journal = {Numerical Linear Algebra with Applications},
      • year = 2002,
      • volume = 9,
      • number = 2,
      • pages = {115--139},
      • note = {Times Cited: 1 Bakhvalov, NS Knyazev, AV Parashkevov, RR}
      • }
    •  A. V. Knyazev and M. E. Argentati, "Principal angles between subspaces in an A-based scalar product: Algorithms and perturbation estimates", Siam Journal on Scientific Computing, Times Cited: 26 Knyazev, AV Argentati, ME, Vol. 23, No. 6, pp. 2008-2040, 2002.
      BibTeX
      • @Article{Knyazev2002,
      • author = {Knyazev, A. V. and Argentati, M. E.},
      • title = {Principal angles between subspaces in an A-based scalar product: Algorithms and perturbation estimates},
      • journal = {Siam Journal on Scientific Computing},
      • year = 2002,
      • volume = 23,
      • number = 6,
      • pages = {2008--2040},
      • note = {Times Cited: 26 Knyazev, AV Argentati, ME}
      • }
    •  A. V. Knyazev, "Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method", Siam Journal on Scientific Computing, Times Cited: 95 Knyazev, AV 6th Copper Mountain Conference APR 03-07, 2000 BOULDER, CO, Vol. 23, No. 2, pp. 517-541, 2001.
      BibTeX
      • @Article{Knyazev2001,
      • author = {Knyazev, A. V.},
      • title = {Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method},
      • journal = {Siam Journal on Scientific Computing},
      • year = 2001,
      • volume = 23,
      • number = 2,
      • pages = {517--541},
      • note = {Times Cited: 95 Knyazev, AV 6th Copper Mountain Conference APR 03-07, 2000 BOULDER, CO}
      • }
    •  Andrew V. Knyazev, "Preconditioned eigensolvers---an oxymoron? %Z Large scale eigenvalue problems (Argonne, IL, 1997)", Electron. Trans. Numer. Anal., Vol. 7, pp. 104-123 (electronic), 1998.
      BibTeX
      • @Article{Knyazev1998,
      • author = {Knyazev, Andrew V.},
      • title = {Preconditioned eigensolvers---an oxymoron? %Z Large scale eigenvalue problems (Argonne, IL, 1997)},
      • journal = {Electron. Trans. Numer. Anal.},
      • year = 1998,
      • volume = 7,
      • pages = {104--123 (electronic)}
      • }
    •  A. V. Knyazev, "New estimates for Ritz vectors", Mathematics of Computation, Times Cited: 16 Knyazev, AV, Vol. 66, No. 219, pp. 985-995, 1997.
      BibTeX
      • @Article{Knyazev1997,
      • author = {Knyazev, A. V.},
      • title = {New estimates for Ritz vectors},
      • journal = {Mathematics of Computation},
      • year = 1997,
      • volume = 66,
      • number = 219,
      • pages = {985--995},
      • note = {Times Cited: 16 Knyazev, AV}
      • }
    •  J. H. Bramble, J. E. Pasciak and A. V. Knyazev, "A subspace preconditioning algorithm for eigenvector/eigenvalue computation", Advances in Computational Mathematics, Times Cited: 33 Bramble, JH Pasciak, JE Knyazev, AV, Vol. 6, No. 2, pp. 159-189, 1996.
      BibTeX
      • @Article{Bramble1996,
      • author = {Bramble, J. H. and Pasciak, J. E. and Knyazev, A. V.},
      • title = {A subspace preconditioning algorithm for eigenvector/eigenvalue computation},
      • journal = {Advances in Computational Mathematics},
      • year = 1996,
      • volume = 6,
      • number = 2,
      • pages = {159--189},
      • note = {Times Cited: 33 Bramble, JH Pasciak, JE Knyazev, AV}
      • }
    •  N. S. Bakhvalov and A. V. Knyazev, "Fictitious domain methods and computation of homogenized properties of composites with a periodic structure of essentially different components", 1994, Numerical methods and applications.
      BibTeX
      • @Inbook{Bakhvalov1994,
      • author = {Bakhvalov, N. S. and Knyazev, A. V.},
      • title = {Fictitious domain methods and computation of homogenized properties of composites with a periodic structure of essentially different components},
      • booktitle = {Numerical methods and applications},
      • year = 1994,
      • pages = {221--266},
      • address = {Boca Raton, FL},
      • publisher = {CRC}
      • }
    •  N. S. Bakhvalov, A. V. Knyazev and M. Eglit, "A Korn-type inequality and orthogonal decompositions in matrix spaces", Russian Acad. Sci. Math. Doklady, Vol. 48, No. 1, pp. 127-129, 1994.
      BibTeX
      • @Article{Bakhvalov1994a,
      • author = {Bakhvalov, N. S. and Knyazev, A. V. and Eglit, M.},
      • title = {A Korn-type inequality and orthogonal decompositions in matrix spaces},
      • journal = {Russian Acad. Sci. Math. Doklady},
      • year = 1994,
      • volume = 48,
      • number = 1,
      • pages = {127--129}
      • }
    •  Nikolai S. Bakhvalov and Andrew V. Knyazev, "Preconditioned iterative methods in a subspace for linear algebraic equations with large jumps in the coefficients", 1994, Domain decomposition methods in scientific and engineering computing (University Park, PA, 1993).
      BibTeX
      • @Inbook{Bakhvalov1994b,
      • author = {Bakhvalov, Nikolai S. and Knyazev, Andrew V.},
      • title = {Preconditioned iterative methods in a subspace for linear algebraic equations with large jumps in the coefficients},
      • booktitle = {Domain decomposition methods in scientific and engineering computing (University Park, PA, 1993)},
      • year = 1994,
      • volume = 180,
      • series = {Contemp. Math.},
      • pages = {157--162},
      • address = {Providence, RI},
      • publisher = {Amer. Math. Soc.}
      • }
    •  A. V. Knyazev and A. L. Skorokhodov, "Preconditioned Gradient-type Iterative Methods In A Subspace For Partial Generalized Symmetrical Eigenvalue Problems", SIAM Journal on Numerical Analysis, Times Cited: 15 KNYAZEV, AV SKOROKHODOV, AL, Vol. 31, No. 4, pp. 1226-1239, 1994.
      BibTeX
      • @Article{Knyazev1994,
      • author = {Knyazev, A. V. and Skorokhodov, A. L.},
      • title = {Preconditioned Gradient-type Iterative Methods In A Subspace For Partial Generalized Symmetrical Eigenvalue Problems},
      • journal = {SIAM Journal on Numerical Analysis},
      • year = 1994,
      • volume = 31,
      • number = 4,
      • pages = {1226--1239},
      • note = {Times Cited: 15 KNYAZEV, AV SKOROKHODOV, AL}
      • }
    •  N. S. Bakhvalov, A. V. Knyazev and M. Eglit, "A Korn-type inequality and orthogonal decompositions in matrix spaces", Dokl. Akad. Nauk, {\`E}, Vol. 331, No. 5, pp. 536-537, 1993.
      BibTeX
      • @Article{Bakhvalov1993,
      • author = {Bakhvalov, N. S. and Knyazev, A. V. and Eglit, M.},
      • title = {A Korn-type inequality and orthogonal decompositions in matrix spaces},
      • journal = {Dokl. Akad. Nauk},
      • year = 1993,
      • volume = 331,
      • number = 5,
      • pages = {536--537},
      • note = {{\`E}}
      • }
    •  A.V. Knyazev and I.S. Sharapov, "Variational Rayleigh quotient iteration methods for symmetric eigenvalue problem", (East-West) Journal of Numerical Mathematics, Vol. 1, No. 2, pp. 121-129, 1993.
      BibTeX
      • @Article{Knyazev1993,
      • author = {Knyazev, A.V. and Sharapov, I.S.},
      • title = {Variational Rayleigh quotient iteration methods for symmetric eigenvalue problem},
      • journal = {(East-West) Journal of Numerical Mathematics},
      • year = 1993,
      • volume = 1,
      • number = 2,
      • pages = {121--129}
      • }
    •  A.V. Knyazev and A.L. Skorokhodov, "Iterative methods of gradient type in a subspace for a partial symmetric generalized eigenvalue problem", Russian Acad. Sci. Dokl. Mat., Vol. 45, pp. 474-478, 1993.
      BibTeX
      • @Article{Knyazev1993a,
      • author = {Knyazev, A.V. and Skorokhodov, A.L.},
      • title = {Iterative methods of gradient type in a subspace for a partial symmetric generalized eigenvalue problem},
      • journal = {Russian Acad. Sci. Dokl. Mat.},
      • year = 1993,
      • volume = 45,
      • pages = {474--478}
      • }
    •  N.S. Bakhvalov and A.V. Knyazev, "An efficient iterative method for solving the Lame equations for almost incompressible media and Stokes' equations", Soviet Math. Doklady, Vol. 44, No. 1, pp. 4-9, 1992.
      BibTeX
      • @Article{Bakhvalov1992,
      • author = {Bakhvalov, N.S. and Knyazev, A.V.},
      • title = {An efficient iterative method for solving the Lame equations for almost incompressible media and Stokes' equations},
      • journal = {Soviet Math. Doklady},
      • year = 1992,
      • volume = 44,
      • number = 1,
      • pages = {4--9}
      • }
    •  E.G. D'yakonov and A.V. Knyazev, "On an iterative method for finding lower eigenvalues", Russian Journal of Numerical Analysis and Mathematical Modelling, Vol. 7, No. 6, pp. 473-486, 1992.
      BibTeX
      • @Article{Dyakonov1992,
      • author = {D'yakonov, E.G. and Knyazev, A.V.},
      • title = {On an iterative method for finding lower eigenvalues},
      • journal = {Russian Journal of Numerical Analysis and Mathematical Modelling},
      • year = 1992,
      • volume = 7,
      • number = 6,
      • pages = {473--486}
      • }
    •  A. V. Knyazev and A. L. Skorokhodov, "Iterative methods of gradient type in a subspace for a partial symmetric generalized eigenvalue problem", Dokl. Akad. Nauk, Vol. 323, No. 6, pp. 1020-1023, 1992.
      BibTeX
      • @Article{Knyazev1992,
      • author = {Knyazev, A. V. and Skorokhodov, A. L.},
      • title = {Iterative methods of gradient type in a subspace for a partial symmetric generalized eigenvalue problem},
      • journal = {Dokl. Akad. Nauk},
      • year = 1992,
      • volume = 323,
      • number = 6,
      • pages = {1020--1023}
      • }
    •  A. V. Knyazev and A. L. Skorokhodov, "The Preconditioned Gradient-type Iterative Methods In A Subspace For Partial Generalized Symmetrical Eigenvalue Problem", Doklady Akademii Nauk, Times Cited: 0 KNYAZEV, AV SKOROKHODOV, AL, Vol. 323, No. 6, pp. 1020-1023, 1992.
      BibTeX
      • @Article{Knyazev1992a,
      • author = {Knyazev, A. V. and Skorokhodov, A. L.},
      • title = {The Preconditioned Gradient-type Iterative Methods In A Subspace For Partial Generalized Symmetrical Eigenvalue Problem},
      • journal = {Doklady Akademii Nauk},
      • year = 1992,
      • volume = 323,
      • number = 6,
      • pages = {1020--1023},
      • note = {Times Cited: 0 KNYAZEV, AV SKOROKHODOV, AL}
      • }
    •  A.V. Knyazev, "A parallel algorithm of subspace iterations and its implementation on a multiprocessor with ring architecture", Russian Journal of Numerical Analysis and Mathematical Modelling, Vol. 7, No. 1, pp. 55-61, 1992.
      BibTeX
      • @Article{Knyazev1992b,
      • author = {Knyazev, A.V.},
      • title = {A parallel algorithm of subspace iterations and its implementation on a multiprocessor with ring architecture},
      • journal = {Russian Journal of Numerical Analysis and Mathematical Modelling},
      • year = 1992,
      • volume = 7,
      • number = 1,
      • pages = {55--61}
      • }
    •  Andrey V. Knyazev, "Iterative solution of PDE with strongly varying coefficients: algebraic version", 1992.
      BibTeX
      • @Misc{Knyazev1992c,
      • author = {Knyazev, Andrey V.},
      • title = {Iterative solution of PDE with strongly varying coefficients: algebraic version},
      • year = 1992,
      • pages = {85--89},
      • publisher = {Elsevier Science Publishers,Amsterdam, The Netherlands}
      • }
    •  N. S. Bakhvalov and A. V. Knyazev, "An Effective Iterative Method For Solution Of Lame Equations For Almost-incompressible Fluids And Stokes Equations", Doklady Akademii Nauk Sssr, Times Cited: 1 BAKHVALOV, NS KNYAZEV, AV, Vol. 319, No. 1, pp. 13-17, 1991.
      BibTeX
      • @Article{Bakhvalov1991,
      • author = {Bakhvalov, N. S. and Knyazev, A. V.},
      • title = {An Effective Iterative Method For Solution Of Lame Equations For Almost-incompressible Fluids And Stokes Equations},
      • journal = {Doklady Akademii Nauk Sssr},
      • year = 1991,
      • volume = 319,
      • number = 1,
      • pages = {13--17},
      • note = {Times Cited: 1 BAKHVALOV, NS KNYAZEV, AV}
      • }
    •  N. S. Bakhvalov and A. V. Knyazev, "Methods for the effective computation of averaged characteristics of composites of periodic structure consisting of essentially different materials", 1991, Computational processes and systems, No. 8 (Russian).
      BibTeX
      • @Inbook{Bakhvalov1991a,
      • author = {Bakhvalov, N. S. and Knyazev, A. V.},
      • title = {Methods for the effective computation of averaged characteristics of composites of periodic structure consisting of essentially different materials},
      • booktitle = {Computational processes and systems, No. 8 (Russian)},
      • year = 1991,
      • pages = {52--94},
      • address = {Moscow},
      • publisher = {``Nauka''}
      • }
    •  N. S. Bakhvalov, A. V. Knyazev and G. M. Kobelkov, "Iterative methods for solving equations with highly varying coefficients", 1991, Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations (Moscow, 1990).
      BibTeX
      • @Inbook{Bakhvalov1991b,
      • author = {Bakhvalov, N. S. and Knyazev, A. V. and Kobelkov, G. M.},
      • title = {Iterative methods for solving equations with highly varying coefficients},
      • booktitle = {Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations (Moscow, 1990)},
      • year = 1991,
      • pages = {197--205},
      • address = {Philadelphia, PA},
      • publisher = {SIAM},
      • note = {{\cprime}}
      • }
    •  N.S. Bakhvalov and A.V. Knyazev, "Efficient computation of averaged characteristics of composites of a periodic structure of essentially different materials", Soviet Math. Doklady, Vol. 42, No. 1, pp. 57-62, 1991.
      BibTeX
      • @Article{Bakhvalov1991c,
      • author = {Bakhvalov, N.S. and Knyazev, A.V.},
      • title = {Efficient computation of averaged characteristics of composites of a periodic structure of essentially different materials},
      • journal = {Soviet Math. Doklady},
      • year = 1991,
      • volume = 42,
      • number = 1,
      • pages = {57--62}
      • }
    •  N.S. Bakhvalov, A.V. Knyazev and G.M. Kobel'kov, "Iterative methods for solving equations with highly varying coefficients", Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations, 1991, pp. 197-205.
      BibTeX
      • @Inproceedings{Bakhvalov1991d,
      • author = {Bakhvalov, N.S. and Knyazev, A.V. and Kobel'kov, G.M.},
      • title = {Iterative methods for solving equations with highly varying coefficients},
      • booktitle = {Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations},
      • year = 1991,
      • pages = {197--205},
      • publisher = {SIAM}
      • }
    •  A. V. Knyazev, "A preconditioned conjugate gradient method for eigenvalue problems and its implementation in a subspace", 1991, Numerical treatment of eigenvalue problems, Vol. 5 (Oberwolfach, 1990).
      BibTeX
      • @Inbook{Knyazev1991,
      • author = {Knyazev, A. V.},
      • title = {A preconditioned conjugate gradient method for eigenvalue problems and its implementation in a subspace},
      • booktitle = {Numerical treatment of eigenvalue problems, Vol.\ 5 (Oberwolfach, 1990)},
      • year = 1991,
      • volume = 96,
      • series = {Internat. Ser. Numer. Math.},
      • pages = {143--154},
      • address = {Basel},
      • publisher = {Birkh\"auser}
      • }
    •  A. V. Knyazev and A. L. Skorokhodov, "On Exact Estimates Of The Convergence Rate Of The Steepest Ascent Method In The Symmetrical Eigenvalue Problem", Linear Algebra and Its Applications, Times Cited: 3 KNYAZEV, AV SKOROKHODOV, AL, Vol. 154, pp. 245-257, 1991.
      BibTeX
      • @Article{Knyazev1991a,
      • author = {Knyazev, A. V. and Skorokhodov, A. L.},
      • title = {On Exact Estimates Of The Convergence Rate Of The Steepest Ascent Method In The Symmetrical Eigenvalue Problem},
      • journal = {Linear Algebra and Its Applications},
      • year = 1991,
      • volume = 154,
      • pages = {245--257},
      • note = {Times Cited: 3 KNYAZEV, AV SKOROKHODOV, AL}
      • }
    •  N. S. Bakhvalov and A. V. Kniazev, "A New Iterative Algorithm For Solution Of Problems Emerging In The Method Of Fictious Fluxes For Elliptic-equations", Doklady Akademii Nauk Sssr, Times Cited: 1 BAKHVALOV, NS KNIAZEV, AV, Vol. 312, No. 4, pp. 783-786, 1990.
      BibTeX
      • @Article{Bakhvalov1990,
      • author = {Bakhvalov, N. S. and Kniazev, A. V.},
      • title = {A New Iterative Algorithm For Solution Of Problems Emerging In The Method Of Fictious Fluxes For Elliptic-equations},
      • journal = {Doklady Akademii Nauk Sssr},
      • year = 1990,
      • volume = 312,
      • number = 4,
      • pages = {783--786},
      • note = {Times Cited: 1 BAKHVALOV, NS KNIAZEV, AV}
      • }
    •  N. S. Bakhvalov and A. V. Kniazev, "Effective Computation Of Averaged Periodic Structure Composites Consisting Of Essentially Different Components", Doklady Akademii Nauk Sssr, Times Cited: 3 BAKHVALOV, NS KNIAZEV, AV, Vol. 313, No. 4, pp. 777-781, 1990.
      BibTeX
      • @Article{Bakhvalov1990a,
      • author = {Bakhvalov, N. S. and Kniazev, A. V.},
      • title = {Effective Computation Of Averaged Periodic Structure Composites Consisting Of Essentially Different Components},
      • journal = {Doklady Akademii Nauk Sssr},
      • year = 1990,
      • volume = 313,
      • number = 4,
      • pages = {777--781},
      • note = {Times Cited: 3 BAKHVALOV, NS KNIAZEV, AV}
      • }
    •  N.S. Bakhvalov and A.V. Knyazev, "A new iterative algorithm for solving problems of the fictitious flow method for elliptic equations", Soviet Math. Doklady, Vol. 41, No. 3, pp. 481-485, 1990.
      BibTeX
      • @Article{Bakhvalov1990b,
      • author = {Bakhvalov, N.S. and Knyazev, A.V.},
      • title = {A new iterative algorithm for solving problems of the fictitious flow method for elliptic equations},
      • journal = {Soviet Math. Doklady},
      • year = 1990,
      • volume = 41,
      • number = 3,
      • pages = {481--485}
      • }
    •  N.S. Bakhvalov and A.V. Knyazev, "A new iterative algorithm for solving the fictitious fluxes method problems for elliptic equations", Equadiff 7: 7th Czechoslovak Conference on Differential Equations and Their Applications, Kurzweil, Jaroslav, Eds., 1990, vol. 118, pp. 225-227.
      BibTeX
      • @Inproceedings{Bakhvalov1990c,
      • author = {Bakhvalov, N.S. and Knyazev, A.V.},
      • title = {A new iterative algorithm for solving the fictitious fluxes method problems for elliptic equations},
      • booktitle = {Equadiff 7: 7th Czechoslovak Conference on Differential Equations and Their Applications},
      • year = 1990,
      • editor = {Kurzweil, Jaroslav},
      • volume = 118,
      • pages = {225--227},
      • publisher = {BSB BG Teubner Verlagsgesellschaft}
      • }
    •  A.V. Knyazev, V.I. Lebedev and A.L. Skorokhodov, "The Temple-Lehmann-type methods in iterative algorithms", 1990.
      BibTeX
      • @Misc{Knyazev1990,
      • author = {Knyazev, A.V. and Lebedev, V.I. and Skorokhodov, A.L.},
      • title = {The Temple-Lehmann-type methods in iterative algorithms},
      • year = 1990,
      • volume = 5,
      • number = {4/5},
      • pages = {265--273}
      • }
    •  AV KNYAZEV and AL SKOROKHODOV, "Preconditioned Iterative Methods In Subspace For Solving Linear-systems With Indefinite Coefficient Matrices And Eigenvalue Problems", Soviet Journal of Numerical Analysis and Mathematical Modelling, Vol. 4, No. 4, pp. 283-310, 1989.
      BibTeX
      • @Article{KNYAZEV1989,
      • author = {KNYAZEV, AV and SKOROKHODOV, AL},
      • title = {Preconditioned Iterative Methods In Subspace For Solving Linear-systems With Indefinite Coefficient Matrices And Eigenvalue Problems},
      • journal = {Soviet Journal of Numerical Analysis and Mathematical Modelling},
      • year = 1989,
      • volume = 4,
      • number = 4,
      • pages = {283--310}
      • }
    •  R. Khorn and Ch. Dzhonson, Matrichnyi analiz, ``Mir'', Translated from the English by Kh.\ D. Ikramov, A. V. Knyazev and E. E. Tyrtyshnikov; Translation edited and with a foreword by Ikramov, 1989.
      BibTeX
      • @Book{Khorn1989,
      • author = {Khorn, R. and Dzhonson, Ch.},
      • title = {Matrichnyi analiz},
      • year = 1989,
      • pages = 656,
      • address = {Moscow},
      • publisher = {``Mir''},
      • note = {Translated from the English by Kh.\ D. Ikramov, A. V. Knyazev and E. E. Tyrtyshnikov; Translation edited and with a foreword by Ikramov}
      • }
    •  R. Gregori and E. Krishnamurti, Bezoshibochnye vychisleniya, ``Mir'', Metody i prilozheniya. [Methods and applications]; Translated from the English by Kh.\ D. Ikramov and A. V. Knyazev; Translation edited and with a foreword by Ikramov, 1988.
      BibTeX
      • @Book{Gregori1988,
      • author = {Gregori, R. and Krishnamurti, E.},
      • title = {Bezoshibochnye vychisleniya},
      • year = 1988,
      • pages = 208,
      • address = {Moscow},
      • publisher = {``Mir''},
      • note = {Metody i prilozheniya. [Methods and applications]; Translated from the English by Kh.\ D. Ikramov and A. V. Knyazev; Translation edited and with a foreword by Ikramov}
      • }
    •  A. V. Knyazev, V. I. Lebedev and A. L. Skorokhodov, Metody Templya--Limanna v iteratsionnykh algoritmakh, vol. 181, Akad. Nauk SSSR Otdel Vychisl. Mat., 1988.
      BibTeX
      • @Book{Knyazev1988,
      • author = {Knyazev, A. V. and Lebedev, V. I. and Skorokhodov, A. L.},
      • title = {Metody Templya--Limanna v iteratsionnykh algoritmakh},
      • year = 1988,
      • volume = 181,
      • pages = 16,
      • address = {Moscow},
      • publisher = {Akad. Nauk SSSR Otdel Vychisl. Mat.}
      • }
    •  A. V. Knyazev and A. L. Skorokhodov, Modifitsirovannye iteratsionnye metody v podprostranstve dlya resheniya sistem uravnenii so znakoneopredelennymi matritsami i spektralnykh zadach, vol. 205, Akad. Nauk SSSR Otdel Vychisl. Mat., 1988.
      BibTeX
      • @Book{Knyazev1988a,
      • author = {Knyazev, A. V. and Skorokhodov, A. L.},
      • title = {Modifitsirovannye iteratsionnye metody v podprostranstve dlya resheniya sistem uravnenii so znakoneopredelennymi matritsami i spektralnykh zadach},
      • year = 1988,
      • volume = 205,
      • pages = 48,
      • address = {Moscow},
      • publisher = {Akad. Nauk SSSR Otdel Vychisl. Mat.}
      • }
    •  A. V. Knyazev and A. L. Skorokhodov, "The Rate Of Convergence Of The Method Of Steepest Descent In A Euclidean Norm", Ussr Computational Mathematics and Mathematical Physics, Times Cited: 0 KNYAZEV, AV SKOROKHODOV, AL, Vol. 28, No. 5, pp. 195-196, 1988.
      BibTeX
      • @Article{Knyazev1988b,
      • author = {Knyazev, A. V. and Skorokhodov, A. L.},
      • title = {The Rate Of Convergence Of The Method Of Steepest Descent In A Euclidean Norm},
      • journal = {Ussr Computational Mathematics and Mathematical Physics},
      • year = 1988,
      • volume = 28,
      • number = 5,
      • pages = {195--196},
      • note = {Times Cited: 0 KNYAZEV, AV SKOROKHODOV, AL}
      • }
    •  A. V. Knyazev and A. L. Skorokhodov, "The rate of convergence of the method of steepest descent in the Euclidean norm", Zh. Vychisl. Mat. i Mat. Fiz., Vol. 28, No. 10, pp. 1577-1578, 1599, 1988.
      BibTeX
      • @Article{Knyazev1988c,
      • author = {Knyazev, A. V. and Skorokhodov, A. L.},
      • title = {The rate of convergence of the method of steepest descent in the Euclidean norm},
      • journal = {Zh. Vychisl. Mat. i Mat. Fiz.},
      • year = 1988,
      • volume = 28,
      • number = 10,
      • pages = {1577--1578, 1599}
      • }
    •  A. V. Knyazev, "A parallel algorithm for iterations of a subspace and its implementation on a computer with ring architecture", 1987, Numerical methods and mathematical modeling (Russian).
      BibTeX
      • @Inbook{Knyazev1987,
      • author = {Knyazev, A. V.},
      • title = {A parallel algorithm for iterations of a subspace and its implementation on a computer with ring architecture},
      • booktitle = {Numerical methods and mathematical modeling (Russian)},
      • year = 1987,
      • pages = {115--123},
      • address = {Moscow},
      • publisher = {Akad. Nauk SSSR Otdel Vychisl. Mat.}
      • }
    •  A. V. Knyazev, "Methods for the derivation of some estimates in a symmetric eigenvalue problem", 1987, Computational processes and systems, No. 5 (Russian).
      BibTeX
      • @Inbook{Knyazev1987a,
      • author = {Knyazev, A. V.},
      • title = {Methods for the derivation of some estimates in a symmetric eigenvalue problem},
      • booktitle = {Computational processes and systems, No.\ 5 (Russian)},
      • year = 1987,
      • pages = {164--173},
      • address = {Moscow},
      • publisher = {``Nauka''}
      • }
    •  A.V. Knyazev, "Convergence rate estimates for iterative methods for a mesh symmetrie eigenvalue problem", Russian Journal of Numerical Analysis and Mathematical Modelling, Vol. 2, No. 5, pp. 371-396, 1987.
      BibTeX
      • @Article{Knyazev1987b,
      • author = {Knyazev, A.V.},
      • title = {Convergence rate estimates for iterative methods for a mesh symmetrie eigenvalue problem},
      • journal = {Russian Journal of Numerical Analysis and Mathematical Modelling},
      • year = 1987,
      • volume = 2,
      • number = 5,
      • pages = {371--396}
      • }
    •  A.V. Knyazev, "On modified gradient methods for eigenvalue problems", Differentsial'nye Uravneniya, No. 4, pp. 715-717, 1987.
      BibTeX
      • @Article{Knyazev1987c,
      • author = {Knyazev, A.V.},
      • title = {On modified gradient methods for eigenvalue problems},
      • journal = {Differentsial'nye Uravneniya},
      • year = 1987,
      • number = 4,
      • pages = {715--717}
      • }
    •  V.S. Apokorina and A.V. Knyazev, "BIPR-5M software code", VANT, ser. Physics and Technology of Nuclear Reactors, No. 5, pp. 34-35, 1986.
      BibTeX
      • @Article{Apokorina1986,
      • author = {Apokorina, V.S. and Knyazev, A.V.},
      • title = {BIPR-5M software code},
      • journal = {VANT, ser. Physics and Technology of Nuclear Reactors},
      • year = 1986,
      • number = 5,
      • pages = {34--35}
      • }
    •  A. V. Knyazev, Computation of eigenvalues and eigenvectors for mesh problems: algorithms and error estimates (In Russian) Vychislenie sobstvennykh znachenii i vektorov v setochnykh zadachakh: algoritmy i otsenki pogreshnosti, Akad. Nauk SSSR Otdel Vychisl. Mat., 1986.
      BibTeX
      • @Book{Knyazev1986,
      • author = {Knyazev, A. V.},
      • title = {Computation of eigenvalues and eigenvectors for mesh problems: algorithms and error estimates (In Russian) Vychislenie sobstvennykh znachenii i vektorov v setochnykh zadachakh: algoritmy i otsenki pogreshnosti},
      • year = 1986,
      • pages = 188,
      • address = {Moscow},
      • publisher = {Akad. Nauk SSSR Otdel Vychisl. Mat.}
      • }
    •  A. V. Knyazev, "An error estimate for the approximation by the Rayleigh-Ritz method to the invariant subspace that corresponds to nearby eigenvalues", 1985, Computer architecture and numerical methods (Russian).
      BibTeX
      • @Inbook{Knyazev1985,
      • author = {Knyazev, A. V.},
      • title = {An error estimate for the approximation by the Rayleigh-Ritz method to the invariant subspace that corresponds to nearby eigenvalues},
      • booktitle = {Computer architecture and numerical methods (Russian)},
      • year = 1985,
      • pages = {16--18},
      • address = {Moscow},
      • publisher = {Akad. Nauk SSSR Otdel Vychisl. Mat.}
      • }
    •  A. V. Knyazev, "Modified gradient methods and their block analogues for the problems $Mu=lambda Lu,M=M^*,L=L^*>0$", 1985, Computer architecture and numerical methods (Russian).
      BibTeX
      • @Inbook{Knyazev1985a,
      • author = {Knyazev, A. V.},
      • title = {Modified gradient methods and their block analogues for the problems $Mu=lambda Lu,M=M^*,L=L^*>0$},
      • booktitle = {Computer architecture and numerical methods (Russian)},
      • year = 1985,
      • pages = {19--32},
      • address = {Moscow},
      • publisher = {Akad. Nauk SSSR Otdel Vychisl. Mat.}
      • }
    •  A. V. Knyazev, "Sharp a priori error estimates for the Rayleigh-Ritz method with no assumptions on fixed sign or compactness", Mat. Zametki, Vol. 38, No. 6, pp. 900-907, 958, 1985.
      BibTeX
      • @Article{Knyazev1985b,
      • author = {Knyazev, A. V.},
      • title = {Sharp a priori error estimates for the Rayleigh-Ritz method with no assumptions on fixed sign or compactness},
      • journal = {Mat. Zametki},
      • year = 1985,
      • volume = 38,
      • number = 6,
      • pages = {900--907, 958}
      • }
    •  A. V. Knyazev, "Sharp a priori error estimates of inequality type in the Rayleigh-Ritz method for symmetric spectral problems without assumptions on sign-definiteness or compactness", 1985, Methods of numerical and applied mathematics (Russian).
      BibTeX
      • @Inbook{Knyazev1985c,
      • author = {Knyazev, A. V.},
      • title = {Sharp a priori error estimates of inequality type in the Rayleigh-Ritz method for symmetric spectral problems without assumptions on sign-definiteness or compactness},
      • booktitle = {Methods of numerical and applied mathematics (Russian)},
      • year = 1985,
      • pages = {74--88},
      • address = {Moscow},
      • publisher = {Akad. Nauk SSSR Vychisl. Tsentr}
      • }
    •  A. V. Knyazev, "Sharp A Priori Error-estimates Of The Rayleigh-ritz Method Without Assumptions Of Fixed Sign Or Compactness", Mathematical Notes, Times Cited: 1 KNYAZEV, AV, Vol. 38, No. 5-6, pp. 998-1002, 1985.
      BibTeX
      • @Article{Knyazev1985d,
      • author = {Knyazev, A. V.},
      • title = {Sharp A Priori Error-estimates Of The Rayleigh-ritz Method Without Assumptions Of Fixed Sign Or Compactness},
      • journal = {Mathematical Notes},
      • year = 1985,
      • volume = 38,
      • number = {5-6},
      • pages = {998--1002},
      • note = {Times Cited: 1 KNYAZEV, AV}
      • }
    •  A. V. Knyazev, "The Kato-Temple block algorithm for the estimation of eigenvalues: justification and application", 1985, Conjugate equations and perturbation theory in problems of mathematical physics (Russian).
      BibTeX
      • @Inbook{Knyazev1985e,
      • author = {Knyazev, A. V.},
      • title = {The Kato-Temple block algorithm for the estimation of eigenvalues: justification and application},
      • booktitle = {Conjugate equations and perturbation theory in problems of mathematical physics (Russian)},
      • year = 1985,
      • pages = {127--135},
      • address = {Moscow},
      • publisher = {Akad. Nauk SSSR Otdel Vychisl. Mat.}
      • }
    •  V. I. Lebedev, N. S. Bakhvalov, V. I. Agoshkov, O. V. Baburin, A. V. Knyazev and V. P. Shutyaev, Parallel Algorithms for Solving Some Stationary Problems of Mathematical Physics, Parallelnye algoritmy resheniya nekotorykh statsionarnykh zadach matematicheskoi fiziki (In Russian) With a preface by G. I. Marchuk, Akad. Nauk SSSR Otdel Vychisl. Mat., 1984.
      BibTeX
      • @Book{Lebedev1984,
      • author = {Lebedev, V. I. and Bakhvalov, N. S. and Agoshkov, V. I. and Baburin, O. V. and Knyazev, A. V. and Shutyaev, V. P.},
      • title = {Parallel Algorithms for Solving Some Stationary Problems of Mathematical Physics, Parallelnye algoritmy resheniya nekotorykh statsionarnykh zadach matematicheskoi fiziki (In Russian) With a preface by G. I. Marchuk},
      • year = 1984,
      • pages = 143,
      • address = {Moscow},
      • publisher = {Akad. Nauk SSSR Otdel Vychisl. Mat.}
      • }
    •  A. V. Knyazev, O nekotorykh dvukhstupenchatykh metodakh nakhozhdeniya granits spektra lineinogo puchka matrits, vol. 3749/16, Inst. Atomn. Energii, 1983.
      BibTeX
      • @Book{Knyazev1983,
      • author = {Knyazev, A. V.},
      • title = {O nekotorykh dvukhstupenchatykh metodakh nakhozhdeniya granits spektra lineinogo puchka matrits},
      • year = 1983,
      • volume = {3749/16},
      • pages = 29,
      • address = {Moscow},
      • publisher = {Inst. Atomn. Energii}
      • }
    •  A. V. Knyazev and V. I. Lebedev, "Estimates for convergence and analysis of the optimality of iterative methods for the simultaneous computation of several eigenvectors", 1983, Computational methods in linear algebra (Russian) (Moscow, 1982).
      BibTeX
      • @Inbook{Knyazev1983a,
      • author = {Knyazev, A. V. and Lebedev, V. I.},
      • title = {Estimates for convergence and analysis of the optimality of iterative methods for the simultaneous computation of several eigenvectors},
      • booktitle = {Computational methods in linear algebra (Russian) (Moscow, 1982)},
      • year = 1983,
      • pages = {94--114},
      • address = {Moscow},
      • publisher = {Akad. Nauk SSSR Otdel Vychisl. Mat.}
      • }
    •  E. G. Dyakonov and A. V. Knyazev, "A group iteration method for finding the lowest eigenvalues", Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet., {\cprime}, No. 2, pp. 29-34, 81, 1982.
      BibTeX
      • @Article{Dyakonov1982,
      • author = {Dyakonov, E. G. and Knyazev, A. V.},
      • title = {A group iteration method for finding the lowest eigenvalues},
      • journal = {Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet.},
      • year = 1982,
      • number = 2,
      • pages = {29--34, 81},
      • note = {{\cprime}}
      • }
    •  E.G. Dyakonov and A.V. Knyazev, "Group iterative method for finding lower-order eigenvalues", Moscow Univ., Ser. 15, Comput. Math. Cyber., No. 2, pp. 32-40, 1982.
      BibTeX
      • @Article{Dfyakonov1982,
      • author = {Dyakonov, E.G. and Knyazev, A.V.},
      • title = {Group iterative method for finding lower-order eigenvalues},
      • journal = {Moscow Univ., Ser. 15, Comput. Math. Cyber.},
      • year = 1982,
      • number = 2,
      • pages = {32--40}
      • }
    •  E. G. Dyakonov and A. V. Knyazev, Ob odnom iteratsionnom metode nakhozhdeniya mladshikh sobstvennykh chisel, vol. 26, Akad. Nauk SSSR Otdel Vychisl. Mat., {\cprime}, 1981.
      BibTeX
      • @Book{Dyakonov1981,
      • author = {Dyakonov, E. G. and Knyazev, A. V.},
      • title = {Ob odnom iteratsionnom metode nakhozhdeniya mladshikh sobstvennykh chisel},
      • year = 1981,
      • volume = 26,
      • pages = 19,
      • address = {Moscow},
      • publisher = {Akad. Nauk SSSR Otdel Vychisl. Mat.},
      • note = {{\cprime}}
      • }