TR2017-078
Recent implementations, applications, and extensions of the Locally Optimal Block Preconditioned Conjugate Gradient method (LOBPCG)
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- , "Recent implementations, applications, and extensions of the Locally Optimal Block Preconditioned Conjugate Gradient method (LOBPCG)", Householder Symposium on Numerical Linear Algebra, June 2017.BibTeX TR2017-078 PDF
- @inproceedings{Knyazev2017jun,
- author = {Knyazev, Andrew},
- title = {Recent implementations, applications, and extensions of the Locally Optimal Block Preconditioned Conjugate Gradient method (LOBPCG)},
- booktitle = {Householder Symposium on Numerical Linear Algebra},
- year = 2017,
- month = jun,
- url = {https://www.merl.com/publications/TR2017-078}
- }
- , "Recent implementations, applications, and extensions of the Locally Optimal Block Preconditioned Conjugate Gradient method (LOBPCG)", Householder Symposium on Numerical Linear Algebra, June 2017.
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Research Areas:
Abstract:
Since introduction [A. Knyazev, Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method, SISC (2001) doi:10.1137/S1064827500366124] and efficient parallel implementation [A. Knyazev et al., Block locally optimal preconditioned eigenvalue xolvers (BLOPEX) in HYPRE and PETSc, SISC (2007) doi:10.1137/060661624], LOBPCG has been used is a wide range of applications in mechanics, material sciences, and data sciences. We review its recent implementations and applications, as well as extensions of the local optimality idea beyond standard eigenvalue problems.
Related News & Events
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NEWS LOBPCG method of Andrew Knyazev used on the K computer in Japan for superconductivity research Date: March 20, 2018
Where: Asian Conference on Supercomputing FrontiersBrief- RIKEN is Japan's largest comprehensive research institution. The RIKEN Center for Computational Science (R-CCS) is the leadership research center in high performance computing and computational science in Japan, operating the K computer in Kobe, Japan, which achieves 602.7 teraflops on the High Performance Gradients (HPCG), making it the world HPCG top.
R-CCS researchers and collaborators in their new paper use the Hubbard model for strongly-correlated electron systems to understand the mechanism behind the superconductivity. To calculate the ground state of the Hamiltonian, they implement on the K computer and successfully test the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method, invented in 2001 by Andrew Knyazev; see his recent review of LOBPCG.
- RIKEN is Japan's largest comprehensive research institution. The RIKEN Center for Computational Science (R-CCS) is the leadership research center in high performance computing and computational science in Japan, operating the K computer in Kobe, Japan, which achieves 602.7 teraflops on the High Performance Gradients (HPCG), making it the world HPCG top.