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Fast verification of solutions of matrix equations
Publikationstyp
Journal Article
Date Issued
2002-02-01
Sprache
English
Author(s)
Institut
TORE-URI
Journal
Volume
90
Issue
4
Start Page
755
End Page
773
Citation
Numerische Mathematik 90 (4): 755-773 (2002-02-01)
Publisher DOI
Scopus ID
Publisher
Springer
In this paper, we are concerned with a matrix equation Ax = b where A is an n × n real matrix and x and b are n-vectors. Assume that an approximate solution x is given together with an approximate LU decomposition. We will present fast algorithms for proving nonsingularity of A and for calculating rigorous error bounds for ∥A b - x̃∥ . The emphasis is on rigour of the bounds. The purpose of this paper is to propose different algorithms, the fastest with 2/3n flops computational cost for the verification step, the same as for the LU decomposition. The presented algorithms exclusively use library routines for LU decomposition and for all other matrix and vector operations. -1 3 ∞
DDC Class
004: Informatik
510: Mathematik