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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.

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

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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
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