Iterative diagonalization of symmetric matrices in mixed precision and its application to electronic structure calculations

Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while keeping 64-bit accuracy. Moreover, most of the computationally ex...

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Bibliographic Details
Published in:Computer physics communications 2012-04, Vol.183 (4), p.980-985
Main Authors: Tsuchida, Eiji, Choe, Yoong-Kee
Format: Article
Language:English
Subjects:
Conjugate gradient method
Diagonalization
Eigenvalues
Electronic structure calculations
Mixed precision
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Summary:Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while keeping 64-bit accuracy. Moreover, most of the computationally expensive operations are performed by level-3 BLAS/LAPACK routines in our implementation, thus leading to optimal performance on most platforms. We also discuss the effectiveness of problem-specific preconditioners which take into account nondiagonal elements.
ISSN:0010-4655
1879-2944
DOI:10.1016/j.cpc.2012.01.002