FGMRES for linear discrete ill-posed problems

Authors:
Keiichi Morikuni;Lothar Reichel;Ken Hayami
Affiliations:
National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan;Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA;National Institute of Informatics, and Department of Informatics, School of Multidisciplinary Sciences, The Graduate University for Advanced Studies, Sokendai, 2-1-2 Hitotsubashi, Chiyoda-ku, Toky ...
Venue:
Applied Numerical Mathematics
Year:
2014

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Abstract

GMRES is one of the most popular iterative methods for the solution of large linear systems of equations. However, GMRES does not always perform well when applied to the solution of linear systems of equations that arise from the discretization of linear ill-posed problems with error-contaminated data represented by the right-hand side. Such linear systems are commonly referred to as linear discrete ill-posed problems. The FGMRES method, proposed by Saad, is a generalization of GMRES that allows larger flexibility in the choice of solution subspace than GMRES. This paper explores application of FGMRES to the solution of linear discrete ill-posed problems. Numerical examples illustrate that FGMRES with a suitably chosen solution subspace may determine approximate solutions of higher quality than commonly applied iterative methods.