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A Robust and Efficient Implementation of LOBPCG
- Source :
- SIAM Journal on Scientific Computing, vol 40, iss 5, Duersch, JA; Shao, M; Yang, C; & Gu, M. (2017). A robust and efficient implementation of LOBPCG. Lawrence Berkeley National Laboratory: Retrieved from: http://www.escholarship.org/uc/item/7c90z1hr
- Publication Year :
- 2018
- Publisher :
- eScholarship, University of California, 2018.
-
Abstract
- 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. 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.
- Subjects :
- math.NA
Stability (learning theory)
Numerical & Computational Mathematics
010103 numerical & computational mathematics
02 engineering and technology
01 natural sciences
Robustness (computer science)
Conjugate gradient method
Convergence (routing)
FOS: Mathematics
0202 electrical engineering, electronic engineering, information engineering
Symmetric matrix
Mathematics - Numerical Analysis
0101 mathematics
Block (data storage)
Mathematics
020203 distributed computing
Numerical and Computational Mathematics
Applied Mathematics
Computation Theory and Mathematics
Numerical Analysis (math.NA)
symmetric eigenvalue problem
LOBPCG
Computational Mathematics
numerical stability
Algorithm
Numerical stability
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- SIAM Journal on Scientific Computing, vol 40, iss 5, Duersch, JA; Shao, M; Yang, C; & Gu, M. (2017). A robust and efficient implementation of LOBPCG. Lawrence Berkeley National Laboratory: Retrieved from: http://www.escholarship.org/uc/item/7c90z1hr
- Accession number :
- edsair.doi.dedup.....5727bcaf0b7e53cc1f7f22efafdf5bc3