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.
2
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
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.
3
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
In this paper we study numerical properties of the Richardson second order method (RS) for solving a linear system Ax = b, where A € Rnxn is infinitysymmetric and positive definite. We consider the standard model of floating point arithmetic (cf. [6], [7], [11]). We prove that the RS-algorithm is numerically stable. This means that the algorithm computes approximations xk to the exact solution x* = A-1b such that the error limfk||xk - x*ll2 ls of order eMcond(A), where eM is the machine precision and cond(A) = ||A || 2 ||A-1|| denotes the condition number of the matrix A.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.