In this paper we consider the parameter dependent class of preconditioners M#ℎ(a, delta,D) defined in the companion paper [6]. The latter was constructed by using information from a Krylov subspace method, adopted to solve the large symmetric linear system Ax = b. We first estimate the condition number of the preconditioned matrix M#ℎ(a, delta,D)A. Then our preconditioners, which are independent of the choice of the Krylov subspace method adopted, proved to be effective also when solving sequences of slowly changing linear systems, in unconstrained optimization and linear algebra frameworks. A numerical experience is provided to give evidence of the performance of M#ℎ(a,delta,D).
A CLASS OF PRECONDITIONERS FOR LARGE INDEFINTIE LINEAR SYSTEMS, AS BY PRODUCT OF KRYLOV SUBSPACE METHODS: PART 2 / G., Fasano; Roma, Massimo. - STAMPA. - 5/2011:(2011), pp. 1-28.
A CLASS OF PRECONDITIONERS FOR LARGE INDEFINTIE LINEAR SYSTEMS, AS BY PRODUCT OF KRYLOV SUBSPACE METHODS: PART 2
ROMA, Massimo
2011
Abstract
In this paper we consider the parameter dependent class of preconditioners M#ℎ(a, delta,D) defined in the companion paper [6]. The latter was constructed by using information from a Krylov subspace method, adopted to solve the large symmetric linear system Ax = b. We first estimate the condition number of the preconditioned matrix M#ℎ(a, delta,D)A. Then our preconditioners, which are independent of the choice of the Krylov subspace method adopted, proved to be effective also when solving sequences of slowly changing linear systems, in unconstrained optimization and linear algebra frameworks. A numerical experience is provided to give evidence of the performance of M#ℎ(a,delta,D).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
