Fast interval matrix multiplication
type: Item
instance of: scholarly article
title: Fast interval matrix multiplication
zbMATH Open document ID: 1264.65065
published in: Numerical Algorithms
publication date: 2012-09-24T00:00:00Z
review text: The author discusses various methods for the multiplication of point and/or interval matrices with interval result. Some are based on new a priori estimates of the error of floating-point matrix products. The amount of overestimation including all rounding errors is analyzed. In particular, algorithms for conversion of infimum-supremum to midpoint-radius representation are studied, one of which is proved to be optimal. All methods are much faster than the classical method because almost no switch of the rounding mode is necessary, and because the methods are based on highly optimized BLAS3 routines. Several possibilities are discussed to trade overestimation against computational effort. Numerical examples are presented focussing in particular on applications using interval matrix multiplications.
reviewed by: Günter Mayer
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65G30
zbMATH DE Number: 6085769
zbMATH Keywords: interval arithmetic
zbMATH Keywords: overestimation
zbMATH Keywords: matrix multiplication
zbMATH Keywords: infimum-supremum representation
zbMATH Keywords: optimal midpoint-radius representation
zbMATH Keywords: interval matrix product
zbMATH Keywords: rmode
zbMATH Keywords: BLAS
zbMATH Keywords: unit in the first place
zbMATH Keywords: error analysis
zbMATH Keywords: numerical examples
author: Siegfried M. Rump
describes a project that uses: ACRITH-XSC
describes a project that uses: INTLIB
describes a project that uses: BLAS
describes a project that uses: C-XSC
describes a project that uses: C-XSC 2.0
describes a project that uses: PROFIL/BIAS
describes a project that uses: INTLAB
describes a project that uses: mctoolbox
MaRDI profile type: Publication
full work available at URL: s11075-011-9524-z
OpenAlex ID: W2126531109
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DOI: 10.1007/S11075-011-9524-Z
description: scientific article; zbMATH DE number 6085769