TR2014-123

Preconditioned Locally Harmonic Residual Method for Computing Interior Eigenpairs of Certain Classes of Hermitian Matrices


    •  Vecharynski, E.; Knyazev, A., "Preconditioned Locally Harmonic Residual Method for Computing Interior Eigenpairs of Certain Classes of Hermitian Matrices," Tech. Rep. TR2014-123, arXiv, November 2014.
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      • @techreport{Vecharynski2014nov,
      • author = {Vecharynski, E. and Knyazev, A.},
      • title = {Preconditioned Locally Harmonic Residual Method for Computing Interior Eigenpairs of Certain Classes of Hermitian Matrices},
      • journal = {arXiv},
      • year = 2014,
      • month = nov,
      • url = {http://www.merl.com/publications/TR2014-123}
      • }
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  • Research Areas:

    Advanced Control Systems, Algorithms, Mechatronics


We propose a Preconditioned Locally Harmonic Residual (PLHR) method for computing several interior eigenpairs of a generalized Hermitian eigenvalue problem, without traditional spectral transformations, matrix factorizations, or inversions. PLHR is based on a short-term recurrence, easily extended to a block form, computing eigenpairs simultaneously. PLHR can take advantage of Hermitian positive definite preconditioning, e.g., based on an approximate inverse of an absolute value of a shifted matrix, introduced in [SISC, 35 (2013), pp. A696-A718]. Our numerical experiments demonstrate that PLHR is efficient and robust for certain classes of large-scale interior eigenvalue problems, involving Laplacian and Hamiltonian operators, especially if memory requirements are tight.