Condition numbers and their condition numbers

D.J. Higham

Research output: Contribution to journalArticle

50 Citations (Scopus)

Abstract

Various normwise relative condition numbers that measure the sensitivity of matrix inversion and the solution of linear systems are characterized. New results are derived for the cases where two common, noninduced matrix norms are used, and where different vector norms are used for the domain and range of the matrix. Condition numbers that respect the structure of symmetric problems are also analyzed. The sensitivity of the condition number itself is then investigated, and we obtain sharp examples of Demmel's general result that for certain problems in numerical analysis 'the condition number of the condition number is the condition number.' Finally, upper bounds are derived for the sensitivity of componentwise condition numbers.
LanguageEnglish
Pages193-214
Number of pages21
JournalLinear Algebra and its Applications
Volume214
DOIs
Publication statusPublished - 1 Jan 1995

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Condition number
Linear systems
Numerical analysis
Matrix Norm
Matrix Inversion
Numerical Analysis
Linear Systems
Upper bound
Norm
Range of data

Keywords

  • normwise relative condition
  • matrix inversion
  • linear systems
  • numerical mathematics
  • vectors

Cite this

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Condition numbers and their condition numbers. / Higham, D.J.

In: Linear Algebra and its Applications, Vol. 214, 01.01.1995, p. 193-214.

Research output: Contribution to journalArticle

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