Symmetric Part Preconditioning for the Conjugate Gradient Method in Hilbert Space

Symmetric Part Preconditioning for the Conjugate Gradient Method in Hilbert Space

On the Rate of Convergence of the Conjugate Gradient Method for Linear Operators in Hilbert Space

Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method

We present a variant of the AINV factorized sparse approximate inverse algorithm which is applicable to any symmetric positive definite matrix. The new preconditioner is breakdownfree and, when used in conjunction with the conjugate gradient method, results in a reliable solver for highly ill-conditioned linear systems. We also investigate an alternative approach to a stable approximate inverse...

Algorithm PREQN Fortran Subroutines for Preconditioning the Conjugate Gradient Method

PREQN is a package of Fortran subroutines for automatically generating pre conditioners for the conjugate gradient method It is designed for solving a sequence of linear systems Aix bi i t where the coe cient matrices Ai are symmetric and positive de nite and vary slowly Problems of this type arise for example in non linear optimization The preconditioners are based on limited memory quasi Newt...

Operator Preconditioning in Hilbert Space

2010 1 Introduction The numerical solution of linear elliptic partial differential equations consists of two main steps: discretization and iteration, where generally some conjugate gradient method is used for solving the finite element discretization of the problem. However, when for elliptic problems the dis-cretization parameter tends to zero, the required number of iterations for a prescrib...