Tight and efficient enclosure of matrix multiplication by using optimized BLAS

Katsuhisa Ozaki*, Takeshi Ogita, Shin'ichi Oishi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)237-248
Number of pages12
JournalNumerical Linear Algebra with Applications
Issue number2
Publication statusPublished - 2011 Mar


  • Interval arithmetic
  • Matrix multiplication
  • Verified numerical computation

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics


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