A Class of Preconditioners for Large Indefinite Linear Systems, as By-Product of Krylov Subspace Methods: Part I
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. 4/2011
We propose a class of preconditioners, which are also tailored for symmetric linear systems from linear algebra and nonconvex optimization. Our preconditioners are specifically suited for large linear systems and may be obtained as by-product of Krylov subspace solvers. Each preconditioner in our class is identified by setting the values of a pair of parameters and a scaling matrix, which are user-dependent, and may be chosen according with the structure of the problem in hand. We provide theoretical properties for our preconditioners. In particular, we show that our preconditioners both shift some eigenvalues of the system matrix to controlled values, and they tend to reduce the modulus of most of the other eigenvalues. In a companion paper we study some structural properties of our class of preconditioners, and report the results on a significant numerical experience.
Number of Pages in PDF File: 18
Keywords: preconditioners, large indefinite linear systems, large scale nonconvex optimization, Krylov subspace methods
JEL Classification: C44, C61
Date posted: April 10, 2012 ; Last revised: October 1, 2012
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