Adaptive solution of infinite linear systems by Krylov subspace methods

Authors:
P. Favati;G. Lotti;O. Menchi;F. Romani
Affiliations:
IIT-CNR Via G. Moruzzi 1, 56124 Pisa, Italy;Mathematics Department, Parma University, Via M. D'Azeglio 85, 43100 Parma, Italy;Computer Science Department, Pisa University, Largo B. Pontecorvo 2, 56127 Pisa, Italy;Computer Science Department, Pisa University, Largo B. Pontecorvo 2, 56127 Pisa, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 5
Cited 0

A numerical approach to cyclic-service queueing models

Queueing Systems: Theory and Applications
A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems

SIAM Journal on Scientific Computing
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion

Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Accuracy and Stability of Numerical Algorithms

Accuracy and Stability of Numerical Algorithms
Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems

Quantified Score

Hi-index	7.29

Visualization

Abstract

In this paper we consider the problem of approximating the solution of infinite linear systems, finitely expressed by a sparse coefficient matrix. We analyse an algorithm based on Krylov subspace methods embedded in an adaptive enlargement scheme. The management of the algorithm is not trivial, due to the irregular convergence behaviour frequently displayed by Krylov subspace methods for nonsymmetric systems. Numerical experiments, carried out on several test problems, indicate that the more robust methods, such as GMRES and QMR, embedded in the adaptive enlargement scheme, exhibit good performances.