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Fast interval matrix multiplication
Publikationstyp
Journal Article
Date Issued
2011-12-21
Sprache
English
Author(s)
Institut
TORE-URI
Journal
Volume
61
Issue
1
Start Page
1
End Page
34
Citation
Numerical Algorithms 1 (61): 1-34 (2012-09-01)
Publisher DOI
Scopus ID
Publisher
Baltzer
Several methods for the multiplication of point and/or interval matrices with interval result are discussed. Some are based on new 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 discussed and analyzed, 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 our methods are based on highly optimized BLAS3 routines. We discuss several possibilities to trade overestimation against computational effort. Numerical examples focussing in particular on applications using interval matrix multiplications are presented. © 2011 Springer Science+Business Media, LLC.
Subjects
BLAS
Error analysis
Infimum-supremum representation
Interval arithmetic
Interval matrix product
Matrix multiplication
Optimal midpoint-radius representation
Overestimation
Rounding mode
Unit in the first place (ufp)
DDC Class
004: Informatik
510: Mathematik