Fast verification of solutions of matrix equations

Shin'Ichi Oishi, Siegfried M. Rump*

*この研究の対応する著者

研究成果: Article査読

37 被引用数 (Scopus)

抄録

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-1 b - x̃∥. The emphasis is on rigour of the bounds. The purpose of this paper is to propose different algorithms, the fastest with 2/3n3 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.

本文言語English
ページ(範囲)755-773
ページ数19
ジャーナルNumerische Mathematik
90
4
DOI
出版ステータスPublished - 2002 2 1

ASJC Scopus subject areas

  • 計算数学
  • 応用数学

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