A method of obtaining verified solutions for linear systems suited for Java

Katsuhisa Ozaki, T. Ogita, S. Miyajima, S. Oishi, S. M. Rump

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Recent development of Java's optimization techniques makes Java one of the most useful programming languages for numerical computations. This paper proposes a numerical method of obtaining verified approximate solutions of linear systems. Usual methods for verified computations use switches of rounding modes defined in IEEE standard 754. However, such switches of rounding modes have not been supported in Java. This method avoids using directed rounding, so that it is implementable on a wide range of programming languages including Java. Numerical experiments using Java illustrate that the method can give a very accurate error bound for an approximate solution of a linear system with almost same computational cost as that for calculating an approximate inverse by the Gaussian elimination.

Original languageEnglish
Pages (from-to)337-344
Number of pages8
JournalJournal of Computational and Applied Mathematics
Volume199
Issue number2
DOIs
Publication statusPublished - 2007 Feb 15
Externally publishedYes

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Linear systems
Switches
Java programming language
Computer programming languages
Numerical methods
Costs
Experiments

Keywords

  • Java
  • Linear system
  • Verified computation

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

A method of obtaining verified solutions for linear systems suited for Java. / Ozaki, Katsuhisa; Ogita, T.; Miyajima, S.; Oishi, S.; Rump, S. M.

In: Journal of Computational and Applied Mathematics, Vol. 199, No. 2, 15.02.2007, p. 337-344.

Research output: Contribution to journalArticle

Ozaki, Katsuhisa ; Ogita, T. ; Miyajima, S. ; Oishi, S. ; Rump, S. M. / A method of obtaining verified solutions for linear systems suited for Java. In: Journal of Computational and Applied Mathematics. 2007 ; Vol. 199, No. 2. pp. 337-344.
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