The adaptive augmented GMRES method for solving ill-posed problems

Nao Kuroiwa, Takashi Nodera

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The GMRES method is an iterative method that provides better solutions when dealing with large linear systems of equations with a non-symmetric coefficient matrix. The GMRES Method generates a Krylov subspace for the solution, and the augmented GMRES method allows augmentation of the Krylov subspaces by a user supplied subspace which represents certain known features of the desired solution. The augmented gmres method performs well with suitable augmentation, but performs poorly with unsuitable augmentation. The adaptive augmented gmres method automatically selects a suitable subspace from a set of candidates supplied by the user. This study shows that this method maintains the performance level of augmented GMRES and lightens the burden it puts on its users. Numerical experiments compare robustness as well as the efficiency of various heuristic strategies.

Original languageEnglish
JournalANZIAM Journal
Volume50
Issue numberSUPPL.
Publication statusPublished - 2008

Fingerprint

GMRES Method
Ill-posed Problem
Augmentation
Krylov Subspace
Subspace
GMRES
Linear system of equations
Numerical Experiment
Heuristics
Robustness
Iteration
Coefficient

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

The adaptive augmented GMRES method for solving ill-posed problems. / Kuroiwa, Nao; Nodera, Takashi.

In: ANZIAM Journal, Vol. 50, No. SUPPL., 2008.

Research output: Contribution to journalArticle

Kuroiwa, N & Nodera, T 2008, 'The adaptive augmented GMRES method for solving ill-posed problems', ANZIAM Journal, vol. 50, no. SUPPL..
Kuroiwa, Nao ; Nodera, Takashi. / The adaptive augmented GMRES method for solving ill-posed problems. In: ANZIAM Journal. 2008 ; Vol. 50, No. SUPPL.
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