Fast enclosure of matrix eigenvalues and singular values via rounding mode controlled computation

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Abstract

Modifications of Bauer-Fike type and Weyl type perturbation theorems are presented for matrix eigenvalue and singular value problems. It is shown that the conditions of the presented theorems can be rigorously checked by floating point computation with rounding mode control. It is stressed that verification programs can be easily constructed on usual numerical softwares like MATLAB. Computational cost of obtaining rigorous error bounds for computed eigenvalues is shown to be 6n3 flops for a real symmetric n×n matrix.

Original languageEnglish
Pages (from-to)133-146
Number of pages14
JournalLinear Algebra and Its Applications
Volume324
Issue number1-3
DOIs
Publication statusPublished - 2001 Feb 15
Externally publishedYes

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Keywords

  • Bauer-Fike type theorem
  • Rounding mode controlled computation
  • Verified eigenvalue computation
  • Weyl type theorem

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis

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