2017 Fiscal Year Final Research Report
Improvement of Convergence and Performance for the Krylov Subspace Methods using High-Precision Arithmetic
| Project/Area Number |
25330141
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
High performance computing
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
石渡 恵美子 東京理科大学, 理学部第一部応用数学科, 教授 (30287958)
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Keywords | 高精度演算 / 混合精度演算 / Double-double演算 / Quad-double演算 / 反復法 / リスタート / 疎行列 / 連立一次方程式 |
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| Outline of Final Research Achievements |
The Krylov Subspace Methods have some problems such as slow convergence rate or divergence, difficulty of parallelization of preconditioners, and rounding errors. The use of High-Precision arithmetic has a possibility to eliminate these problems, however it's costly.
We choose Double-double and Quad-double arithmetics as High-Precision arithmetic. The use of High-Precision arithmetic improved iterative process in Krylov Subspace methods, but did not improve a tridiagonalization process in Lanczos tridiagonalization method. From these results, the use of High-Precision arithmetic is effective for many algorithms, but not for all. To reduce computation cost, we combined three different arithmetic precisions such as double, Double-double, and Quad-double. There are many kind of combinations, and some of them were practically effective, but there was no method to fit for all test problems. As a software library we should resolve a problem how to relate combination methods and test problems.
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| Free Research Field |
コンピュータサイエンス
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