Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method
Authors:
- Michele BenziMBMichele Benzi
- Jane K. CullumJCJane K. Cullum
- Miroslav TumaMTMiroslav Tuma
- 1 January 2000
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Scientific Computing
- Vol. 22 (4) , 1318-1332
Abstract
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 breakdown-free 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, based on the idea of diagonally compensated reduction of matrix entries. The results of numerical tests on challenging linear systems arising from finite element modeling of elasticity and diffusion problems are presented.Keywords
This publication has 29 references indexed in Scilit:
- Approximate inverse preconditioning in the parallel solution of sparse eigenproblemsNumerical Linear Algebra with Applications, 2000
- Orderings for Factorized Sparse Approximate Inverse PreconditionersSIAM Journal on Scientific Computing, 2000
- A comparative study of sparse approximate inverse preconditionersApplied Numerical Mathematics, 1999
- An MPI Implementation of the SPAI Preconditioner on the T3EThe International Journal of High Performance Computing Applications, 1999
- An assessment of some preconditioning techniques in shell problemsCommunications in Numerical Methods in Engineering, 1998
- Numerical experiments with two approximate inverse preconditionersBIT Numerical Mathematics, 1998
- A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear SystemsSIAM Journal on Scientific Computing, 1998
- A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient MethodSIAM Journal on Scientific Computing, 1996
- Diagonally compensated reduction and related preconditioning methodsNumerical Linear Algebra with Applications, 1994
- A robust incomplete Choleski‐conjugate gradient algorithmInternational Journal for Numerical Methods in Engineering, 1984