Improved Accuracy and Parallelism for MRRR-Based Eigensolvers -- A Mixed Precision Approach
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Other documents of the author: Petschow, Matthias; Quintana-Orti, Enrique S.; Bientinesi, Paolo
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comunitat-uji-handle2:10234/7036
comunitat-uji-handle3:10234/8620
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Title
Improved Accuracy and Parallelism for MRRR-Based Eigensolvers -- A Mixed Precision ApproachDate
2014Publisher
Society for Industrial and Applied MathematicsBibliographic citation
PETSCHOW, M.; QUINTANA-ORTÍ, E. S.; BIENTINESI, P. Improved Accuracy and Parallelism for MRRR-Based Eigensolvers---A Mixed Precision Approach. SIAM Journal on Scientific Computing, 2014, 36.2: C240-C263.Type
info:eu-repo/semantics/articlePublisher version
http://epubs.siam.org/doi/abs/10.1137/130911561Subject
Abstract
The real symmetric tridiagonal eigenproblem is of outstanding importance in numerical computations; it arises frequently as part of eigensolvers for standard and generalized dense Hermitian eigenproblems that are based ... [+]
The real symmetric tridiagonal eigenproblem is of outstanding importance in numerical computations; it arises frequently as part of eigensolvers for standard and generalized dense Hermitian eigenproblems that are based on a reduction to real tridiagonal form. For its solution, the algorithm of multiple relatively robust representations (MRRR) is among the fastest methods. Although fast, the solvers based on MRRR do not deliver the same accuracy as competing methods like Divide & Conquer or the QR algorithm. In this paper, we demonstrate that the use of mixed precisions leads to improved accuracy of MRRR-based eigensolvers with limited or no performance penalty. As a result, we obtain eigensolvers that are not only as accurate as or more accurate than the best available methods, but also---under most circumstances---faster and more scalable than the competition. [-]
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SIAM Journal on Scientific Computing, 2014, 36.2Rights
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