Fast algorithms for floating-point interval matrix multiplication

Katsuhisa Ozaki, Takeshi Ogita, Siegfried M. Rump, Shin'Ichi Oishi

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We discuss several methods for real interval matrix multiplication. First, earlier studies of fast algorithms for interval matrix multiplication are introduced: naive interval arithmetic, interval arithmetic by midpointradius form by OishiRump and its fast variant by OgitaOishi. Next, three new and fast algorithms are developed. The proposed algorithms require one, two or three matrix products, respectively. The point is that our algorithms quickly predict which terms become dominant radii in interval computations. We propose a hybrid method to predict which algorithm is suitable for optimizing performance and width of the result. Numerical examples are presented to show the efficiency of the proposed algorithms.

Original languageEnglish
Pages (from-to)1795-1814
Number of pages20
JournalJournal of Computational and Applied Mathematics
Volume236
Issue number7
DOIs
Publication statusPublished - 2012 Jan

Keywords

  • Interval arithmetic
  • INTLAB
  • Matrix multiplication
  • Verified numerical computations

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

Fast algorithms for floating-point interval matrix multiplication. / Ozaki, Katsuhisa; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin'Ichi.

In: Journal of Computational and Applied Mathematics, Vol. 236, No. 7, 01.2012, p. 1795-1814.

Research output: Contribution to journalArticle

Ozaki, Katsuhisa ; Ogita, Takeshi ; Rump, Siegfried M. ; Oishi, Shin'Ichi. / Fast algorithms for floating-point interval matrix multiplication. In: Journal of Computational and Applied Mathematics. 2012 ; Vol. 236, No. 7. pp. 1795-1814.
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