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Tight and efficient enclosure of matrix multiplication by using optimized BLAS
Author(s) -
Ozaki Katsuhisa,
Ogita Takeshi,
Oishi Shin'ichi
Publication year - 2011
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.724
Subject(s) - multiplication (music) , enclosure , matrix (chemical analysis) , matrix multiplication , floating point , algorithm , mathematics , multiplication algorithm , point (geometry) , interval (graph theory) , interval arithmetic , arithmetic , computer science , combinatorics , geometry , mathematical analysis , telecommunications , materials science , physics , quantum mechanics , binary number , composite material , quantum , bounded function
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. Copyright © 2010 John Wiley & Sons, Ltd.