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Numerical solutions of symmetric saddle point problem by direct methods

Smoktunowicz A., Okulicka-Dłużewska F.

Demonstratio Mathematica

2013

Vol. 46, nr 3

437--451

Numerical stability of two main direct methods for solving the symmetric saddle point problem are analyzed. The first one is a generalization of Golub’s method for the augmented system formulation (ASF) and uses the Householder QR decomposition. The second method is supported by the singular value decomposition (SVD). Numerical comparison of some direct methods are given.

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

Szularz M., Smoktunowicz A., Pawelec E.

Demonstratio Mathematica

2010

Vol. 43, nr 4

755-763

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.