Average condition number for solving linear equations
type: Item
instance of: scholarly article
title: Average condition number for solving linear equations
zbMATH Open document ID: 0603.65025
DOI: 10.1016/0024-3795(86)90266-1
author: B. George
published in: Linear Algebra and its Applications
publication date: 1986-01-01T00:00:00Z
review text: This is a statistical consideration of the condition number of a disturbed system of linear equations \(Ax=b\). For a Lebesgue-measure \(\mu\) it is shown, that the average condition number in \(L_ p\) is comparable with the worst case condition number. For the Frobenius norm one gains about \(\log_ 2n+0.9\) bits on the average as compared to the worst case, n being the dimension of the linear system. Beside the Frobenius norm componentwise perturbations and the spectral norm are considered. Finally it is indicated how the result can be extended for perturbations of both A and b.
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 15A12
Mathematics Subject Classification ID: 15A60
zbMATH DE Number: 3974174
zbMATH Keywords: disturbed system
zbMATH Keywords: average condition number
zbMATH Keywords: worst case
zbMATH Keywords: Frobenius norm
zbMATH Keywords: spectral norm
MaRDI profile type: Publication
full work available at URL: 0024-3795(86)90266-1
OpenAlex ID: W2018239771
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cites work: Q4139189
cites work: Iterative Refinement Implies Numerical Stability for Gaussian Elimination
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description: scientific article; zbMATH DE number 3974174