Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: A Robust and Efficient Implementation of LOBPCG

Journal Article · · SIAM Journal on Scientific Computing
DOI: https://doi.org/10.1137/17M1129830 · OSTI ID:1525270
 [1]; ORCiD logo [2];  [2];  [3]
  1. Univ. of California, Berkeley, CA (United States). Dept. of Mathematics
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.
  3. Univ. of California, Berkeley, CA (United States). Dept. of Mathematics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.
+ Show Author Affiliations

Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) is widely used to compute eigenvalues of large sparse symmetric matrices. The algorithm can suffer from numerical instability if it is not implemented with care. This is especially problematic when the number of eigenpairs to be computed is relatively large. In this paper we propose an improved basis selection strategy based on earlier work by Hetmaniuk and Lehoucq as well as a robust convergence criterion which is backward stable to enhance the robustness. Here, we also suggest several algorithmic optimizations that improve performance of practical LOBPCG implementations. Numerical examples confirm that our approach consistently and significantly outperforms previous competing approaches in both stability and speed.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1525270
Journal Information:
SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 5 Vol. 40; ISSN 1064-8275
Publisher:
SIAMCopyright Statement
Country of Publication:
United States
Language:
English

References (12)

Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver journal January 2018
Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method journal January 2001
Anasazi software for the numerical solution of large-scale eigenvalue problems journal July 2009
The SIESTA method for ab initio order- N materials simulation journal March 2002
Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in Hypre and PETSc journal January 2007
Communication lower bounds and optimal algorithms for numerical linear algebra journal May 2014
A High Performance Block Eigensolver for Nuclear Configuration Interaction Calculations journal June 2017
Basis selection in LOBPCG journal October 2006
PARSEC – the pseudopotential algorithm for real-space electronic structure calculations: recent advances and novel applications to nano-structures journal April 2006
An overview of the sparse basic linear algebra subprograms: The new standard from the BLAS technical forum journal June 2002
Basic Linear Algebra Subprograms for Fortran Usage journal September 1979
A Block Orthogonalization Procedure with Constant Synchronization Requirements journal January 2002

Cited By (1)

A Scalable Matrix-Free Iterative Eigensolver for Studying Many-Body Localization
  • Van Beeumen, Roel; Kahanamoku-Meyer, Gregory D.; Yao, Norman Y.
  • HPCAsia2020: International Conference on High Performance Computing in Asia-Pacific Region, Proceedings of the International Conference on High Performance Computing in Asia-Pacific Region https://doi.org/10.1145/3368474.3368497
conference January 2020

Similar Records

Related Subjects

97 MATHEMATICS AND COMPUTING
symmetric eigenvalue problem
LOBPCG
numerical stability