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A note on backward errors for structured linear systems
Umeå University, Faculty of Science and Technology, Departement of Computing Science.
2005 (English)In: Numerical Linear Algebra with Applications, Vol. 12, no 7, 585-603 p.Article in journal (Refereed) Published
Abstract [en]

Let (x) over tilde be a computed solution to a linear system Ax = b with A is an element of A, where A is a proper subclass of matrices in R-nxn. A structured backward error (SBE) eta(A)((x) over tilde) of (x) over tilde is defined by a measure of the minimal perturbations Delta A and Delta b such that (A + Delta A)(x) over tilde = b + Delta b with A + Delta A is an element of A and that the SBE eta(A)((x) over tilde) can be used to distinguish the structured backward stability of the computed solution (x) over tilde. For simplicity, we may define a partial SBE eta(A,0)((x) over tilde) of (x) over tilde by a measure of the minimal perturbation Delta A(*) such that (A + Delta A(*))(x) over tilde = b with A + Delta A(*)is an element of A Can one use the partial SBE to distinguish the structured backward stability of (x) over tilde? In this note we show that the partial SBE eta(A,0)((x) over tilde) may be much larger than the SBE eta(A)((x) over tilde) for certain structured linear systems such as symmetric Toeplitz systems, KKT systems, and dual Vandermonde systems. Besides, certain backward errors for linear least squares are discussed. Copyright (c) 2004 John Wiley & Sons, Ltd.

Place, publisher, year, edition, pages
2005. Vol. 12, no 7, 585-603 p.
Identifiers
URN: urn:nbn:se:umu:diva-22015ISBN: 1070-5325 OAI: oai:DiVA.org:umu-22015DiVA: diva2:212278
Available from: 2009-04-21 Created: 2009-04-21 Last updated: 2009-04-21

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