Tight and efficient enclosure of matrix multiplication by using optimized BLAS

Katsuhisa Ozaki*, Takeshi Ogita, Shin'ichi Oishi

*この研究の対応する著者

研究成果: Article査読

9 被引用数 (Scopus)

抄録

This paper is concerned with the tight enclosure of matrix multiplication AB for two floating-point matrices A and B. The aim of this paper is to compute component-wise upper and lower bounds of the exact result C of the matrix multiplication AB by floating-point arithmetic. Namely, an interval matrix enclosing C is obtained. In this paper, new algorithms for enclosing C are proposed. The proposed algorithms are designed to mainly exploit the level 3 operations in BLAS. Although the proposed algorithms take around twice as much costs as a standard algorithm promoted by Oishi and Rump, the accuracy of the result by the proposed algorithms is better than that of the standard algorithm. At the end of this paper, we present numerical examples showing the efficiency of the proposed algorithms.

本文言語English
ページ(範囲)237-248
ページ数12
ジャーナルNumerical Linear Algebra with Applications
18
2
DOI
出版ステータスPublished - 2011 3

ASJC Scopus subject areas

  • 代数と数論
  • 応用数学

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