Corrigendum: Block Preconditioning for the Conjugate Gradient Method

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...

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 ...

A conjugate gradient based method for Decision Neural Network training

Decision Neural Network is a new approach for solving multi-objective decision-making problems based on artificial neural networks. Using inaccurate evaluation data, network training has improved and the number of educational data sets has decreased. The available training method is based on the gradient decent method (BP). One of its limitations is related to its convergence speed. Therefore,...

Conjugate-Gradient Preconditioning Methods: Numerical Results