Iterative Methods with Preconditioners for Indefinite Systems

Abstract

For the sparse linear equations $Kx=b$, where $K$ arising from optimization and discretization of some PDEs is symmetric and indefinite, it is shown that the $L \overline{L}^T $ factorization can be used to provide an "exact" preconditioner for SYMMLQ and UZAWA algorithms. "Inexact" preconditioner derived from approximate factorization is used in the numerical experiments.