Explicit conjugate gradient method with preconditioning

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...

Conjugate-Gradient Preconditioning Methods: Numerical Results

Nonsymmetric multigrid preconditioning for conjugate gradient methods

We numerically analyze the possibility of turning off post-smoothing (relaxation) in geometric multigrid used as a preconditioner in conjugate gradient linear and eigenvalue solvers for the 3D Laplacian. The geometric Semicoarsening Multigrid (SMG) method is provided by the hypre parallel software package. We solve linear systems using two variants (standard and flexible) of the preconditioned ...

Steepest Descent and Conjugate Gradient Methods with Variable Preconditioning

We analyze the conjugate gradient (CG) method with variable preconditioning for solving a linear system with a real symmetric positive definite (SPD) matrix of coefficients A. We assume that the preconditioner is SPD on each step, and that the condition number of the preconditioned system matrix is bounded above by a constant independent of the step number. We show that the CG method with varia...