Verified Numerical Computations for Large-Scale Linear Systems

Katsuhisa Ozaki, Takeshi Terao, Takeshi Ogita, Takahiro Katagiri

Research output: Contribution to journalArticlepeer-review

Abstract

This paper concerns accuracy-guaranteed numerical computations for linear systems. Due to the rapid progress of supercomputers, the treatable problem size is getting larger. The larger the problem size, the more rounding errors in floating-point arithmetic can accumulate in general, and the more inaccurate numerical solutions are obtained. Therefore, it is important to verify the accuracy of numerical solutions. Verified numerical computations are used to produce error bounds on numerical solutions. We report the implementation of a verification method for large-scale linear systems and some numerical results using the RIKEN K computer and the Fujitsu PRIMEHPC FX100, which show the high performance of the verified numerical computations.

Original languageEnglish
Pages (from-to)269-285
Number of pages17
JournalApplications of Mathematics
Volume66
Issue number2
DOIs
Publication statusPublished - 2021 Apr

Keywords

  • 65G20
  • 65G50
  • 65Y05
  • floating-point arithmetic
  • high-performance computing
  • large-scale linear system
  • verified numerical computation

ASJC Scopus subject areas

  • Applied Mathematics

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