A Class of Preconditioners for Large Indefinite Linear Systems, as By-Product of Krylov Subspace Methods: Part II
Ca Foscari University of Venice - Department of Management
University of Rome I - Department of Computer and Systems Science
July 1, 2011
Department of Management, Università Ca' Foscari Venezia Working Paper No. 5/2011
In this paper we consider the parameter dependent class of preconditioners M(a,d,D) defined in the companion paper 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(a,d,D). 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(a,d,D).
Number of Pages in PDF File: 31
Keywords: pre conditioners, large indefinite linear systems, large scale non convex optimization, Krylov subspace methods
JEL Classification: C44, C61working papers series
Date posted: April 10, 2012 ; Last revised: October 1, 2012
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