Iterative diagonalization of symmetric matrices in mixed precision and its application to electronic structure calculations |
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| Authors: | Eiji Tsuchida Yoong-Kee Choe |
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| Affiliation: | 1. King Abdullah University of Technology and Science, Thuwal, K.S.A;2. Reservoir Engineering Research Institute, Palo Alto, California, U.S.A.;3. Effat University, Jeddah, K.S.A;1. Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vodárenskou vě?í 2, CZ-182 07 Prague 8, Czech Republic;2. Faculty of Mathematics and Information Science, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland;3. Technical University of Liberec, Department of Mathematics, Studentská 2, CZ-461 17 Liberec, Czech Republic;1. State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, China;2. College of Materials Science and Engineering, Jilin University, Changchun 130012, China;3. Department of Chemistry and Biochemistry, California State University Northridge, 18111 Nordhoff St., Northridge, CA 91330, USA |
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| Abstract: | 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. |
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