Generalized Augmented Matrix Preconditioning Approach and its Application to Iterative Solution of Ill-Conditioned Algebraic Systems

Authors:
Alexander Padiy;Owe Axelsson;Ben Polman
Affiliations:
-;-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2000

Citing 0
Cited 9

Preconditioning techniques for large linear systems: a survey

Journal of Computational Physics
Optimizing Two-Level Preconditionings for the Conjugate Gradient Method

LSSC '01 Proceedings of the Third International Conference on Large-Scale Scientific Computing-Revised Papers
Iteration number for the conjugate gradient method

Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
Fast and robust solvers for pressure-correction in bubbly flow problems

Journal of Computational Physics
An Efficient Newton-Krylov Implementation of the Constrained Runs Scheme for Initializing on a Slow Manifold

Journal of Scientific Computing
Comparison of Two-Level Preconditioners Derived from Deflation, Domain Decomposition and Multigrid Methods

Journal of Scientific Computing
Milestones in the development of iterative solution methods

Journal on Image and Video Processing - Special issue on iterative signal processing in communications
A Coarse Space Construction Based on Local Dirichlet-to-Neumann Maps

SIAM Journal on Scientific Computing
Further comparison of additive and multiplicative coarse grid correction

Applied Numerical Mathematics

Quantified Score

Hi-index	0.01

Visualization

Abstract

The present work is devoted to a class of preconditioners based on the augmented matrix approach considered earlier by two of the present authors. It presents some generalizations of the subspace-correction schemes studied earlier and gives a brief comparison of the developed technique with a somewhat similar "deflation" algorithm.The developed preconditioners are able to improve significantly an eigenvalue distribution of certain severely ill-conditioned algebraic systems by using properly chosen projection matrices, which correct the low-frequency components in the spectrum. One of the main advantages of the proposed approach is the possibility of using inexact solvers within the projectors. Another attractive feature of the developed method is that it can be easily combined with other preconditioners, for instance, those which correct the high-frequency eigenmodes.