A Comparative Study of Iterative Solvers Exploiting Spectral Information for SPD Systems

L. Giraud, D. Ruiz, A.Touhami

CERFACS and ENSEEIHT-IRIT, France


Abstract
We intend to solve the linear system Ax=b where A is large sparse and symmetric positive definite. We consider solution techniques that exploit spectral information about the matrix A. In this talk, we will describe the various techniques as well as the observed numerical behaviours on a set of model problems from Matrix Market. We will discuss their numerical efficiency, computational complexity and sensitivity to the accuracy of the spectral information.

Keywords: Chebyshev polynomial, Block Lanczos method, filtering, deflation, preconditioning, iterative methods.