Verified numerical computations for dense linear systems in supercomputing

研究成果: Conference article

抄録

The numerical computations with guaranteed accuracy called verified numerical computations are studied, herein. We focus on an accurate numerical solution for dense linear systems of the form Ax = b and error bound of in supercomputing, where is an approximate solution. First, we implemented accurate algorithms for a matrix-vector product for parallel and distributed computing, and then, applied them to iterative refinements. Next, we implemented verified numerical computations using the Parallel Basic Linear Algebra Subprograms (PBLAS) and the Scalable Linear Algebra Package library (ScaLAPACK). Numerical examples of the verified numerical computations for linear systems are presented using the Fujitsu FX100 supercomputer. They clearly illustrate the efficiency of the verified numerical computations.

元の言語English
記事番号012014
ジャーナルJournal of Physics: Conference Series
1218
発行部数1
DOI
出版物ステータスPublished - 2019 5 31
イベント3rd International Conference on Mathematics; Pure, Applied and Computation, ICoMPAC 2018 - Surabaya, Indonesia
継続期間: 2018 10 20 → …

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linear systems
algebra
supercomputers
products

ASJC Scopus subject areas

  • Physics and Astronomy(all)

これを引用

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abstract = "The numerical computations with guaranteed accuracy called verified numerical computations are studied, herein. We focus on an accurate numerical solution for dense linear systems of the form Ax = b and error bound of in supercomputing, where is an approximate solution. First, we implemented accurate algorithms for a matrix-vector product for parallel and distributed computing, and then, applied them to iterative refinements. Next, we implemented verified numerical computations using the Parallel Basic Linear Algebra Subprograms (PBLAS) and the Scalable Linear Algebra Package library (ScaLAPACK). Numerical examples of the verified numerical computations for linear systems are presented using the Fujitsu FX100 supercomputer. They clearly illustrate the efficiency of the verified numerical computations.",
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