Fast inclusion of interval matrix multiplication

Takeshi Ogita; Shin'ichi Oishi

doi:10.1007/s11155-005-3615-2

Fast inclusion of interval matrix multiplication

Takeshi Ogita^*, Shin'ichi Oishi

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

This paper is concerned with interval matrix multiplication.New algorithms are proposed to calculate an inclusion of the product of interval matrices using rounding mode controlled computation. Thecomputational cost of the proposed algorithms is almost the same as that for calculating an inclusion of the product of point matrices.Numerical results are presented to illustrate that the new algorithms are much faster than the conventional algorithms and that the guaranteed accuracies obtained by the proposed algorithms are comparable to those of the conventional algorithms.

Original language	English
Pages (from-to)	191-205
Number of pages	15
Journal	Reliable Computing
Volume	11
Issue number	3
DOIs	https://doi.org/10.1007/s11155-005-3615-2
Publication status	Published - 2005 Jun

ASJC Scopus subject areas

Software
Computational Mathematics
Applied Mathematics

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10.1007/s11155-005-3615-2

Cite this

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abstract = "This paper is concerned with interval matrix multiplication.New algorithms are proposed to calculate an inclusion of the product of interval matrices using rounding mode controlled computation. Thecomputational cost of the proposed algorithms is almost the same as that for calculating an inclusion of the product of point matrices.Numerical results are presented to illustrate that the new algorithms are much faster than the conventional algorithms and that the guaranteed accuracies obtained by the proposed algorithms are comparable to those of the conventional algorithms.",

author = "Takeshi Ogita and Shin'ichi Oishi",

note = "Funding Information: The authors would like to express their sincere thanks to Prof. S. M. Rump for his stimulating discussions. This research was partially supported by 21st Century COE Program (Productive ICT Academia Program, Waseda University) from the Ministry of Education, Science, Sports, and Culture, Japan.",

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AU - Oishi, Shin'ichi

N1 - Funding Information: The authors would like to express their sincere thanks to Prof. S. M. Rump for his stimulating discussions. This research was partially supported by 21st Century COE Program (Productive ICT Academia Program, Waseda University) from the Ministry of Education, Science, Sports, and Culture, Japan.

PY - 2005/6

Y1 - 2005/6

N2 - This paper is concerned with interval matrix multiplication.New algorithms are proposed to calculate an inclusion of the product of interval matrices using rounding mode controlled computation. Thecomputational cost of the proposed algorithms is almost the same as that for calculating an inclusion of the product of point matrices.Numerical results are presented to illustrate that the new algorithms are much faster than the conventional algorithms and that the guaranteed accuracies obtained by the proposed algorithms are comparable to those of the conventional algorithms.

AB - This paper is concerned with interval matrix multiplication.New algorithms are proposed to calculate an inclusion of the product of interval matrices using rounding mode controlled computation. Thecomputational cost of the proposed algorithms is almost the same as that for calculating an inclusion of the product of point matrices.Numerical results are presented to illustrate that the new algorithms are much faster than the conventional algorithms and that the guaranteed accuracies obtained by the proposed algorithms are comparable to those of the conventional algorithms.

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Fast inclusion of interval matrix multiplication

Abstract

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