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The paper deals with the following inverse perturbation problem for the linear system ATAx = b: assuming that there exist two (possibly different) perturbations E1 and E2 of A so that (A + E2)T (A + E1)y = b, we ask whether there is a single perturbation F of A so that (A + F)T (A + F)y = b. We consider only small relative normwise perturbations of A. It is shown that if yT b >0 and (...) is small, then our problem has a solution. Some practical upper and lower error bounds for the structured backward error are also given.
Wydawca
Czasopismo
Rocznik
Tom
Strony
755--763
Opis fizyczny
Bibliogr. 5 poz., tab.
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autor
autor
autor
- School of Computing and Information Engineering University of Ulster Coleraine Bt52 1sa, Northern Ireland, Marek@infc.ulst.ac.uk
Bibliografia
- [1] Å. Björck, C. C. Paige, Solution of augmented linear systems using orthogonal factorizations, BIT 34 (1994), 1–24.
- [2] V. Frayssé, S. Gratton, V. Toumazou, Structured backward error and condition number for linear systems of the type A*Ax = b, BIT 40 (2000), 74–83.
- [3] V. Frayssé, S. Gratton, V. Toumazou, On a structured backward error analysis for linear systems of the type A*Ax = b, CERFACS Technical Report TR/PA/98/01.
- [4] J.-G. Sun, Structured backward error for the linear system ATAx = b, Journal of Natural Sciences of Heilongjiang University 21, 4 (2004), 4–10 (English version).
- [5] J.-G. Sun, A note on backward errors for structured linear systems, Numer. Lineał Algebra Appl. 12 (2005), 585–603.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0031-0003