Acceleration of a preconditioning method for ill-conditioned dense linear systems by use of a BLAS-based method

Yuka Kobayashi, Takeshi Ogita, Katsuhisa Ozaki

Research output: Research - peer-reviewArticle

Abstract

We are interested in accurate numerical solutions of ill-conditioned linear systems using floating-point arithmetic. Recently, we proposed a preconditioning method to reduce the condition numbers of coefficient matrices. The method utilizes an LU factorization obtained in working precision arithmetic and requires matrix multiplication in quadruple precision arithmetic. In this note, we aim to accelerate the preconditioning method from a practical point of view. For this purpose, we apply a more efficient method of accurate matrix multiplication based on BLAS in the preconditioning method. We demonstrate excellent performance of the BLAS-based preconditioning method by numerical experiments.

LanguageEnglish
Pages15-23
Number of pages9
JournalReliable Computing
Volume25
StatePublished - 2017

Fingerprint

Linear systems
Digital arithmetic
Factorization
Experiments

Keywords

  • Floating-point arithmetic
  • Ill-conditioned linear systems
  • Preconditioning method

ASJC Scopus subject areas

  • Software
  • Computational Mathematics
  • Applied Mathematics

Cite this

Acceleration of a preconditioning method for ill-conditioned dense linear systems by use of a BLAS-based method. / Kobayashi, Yuka; Ogita, Takeshi; Ozaki, Katsuhisa.

In: Reliable Computing, Vol. 25, 2017, p. 15-23.

Research output: Research - peer-reviewArticle

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