An inverse structured perturbation problem for the linear system ATAx = b

• Autorzy: Szularz M. , Smoktunowicz A. , Pawelec E.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Moore-Penrose inverse; structured linear system; backward error; condition number; structured backward stability

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2010
• Tom: Vol. 43, nr 4
• Strony: 755--763
• Opis fizyczny: Bibliogr. 5 poz., tab.

Twórcy

autor

Szularz M.

autor

Smoktunowicz A.

autor

Pawelec E.

• School of Computing and Information Engineering University of Ulster Coleraine Bt52 1sa, Northern Ireland,

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.