Range-space variants and inexact matrix-vector products in Krylov solvers for linear systems arising from inverse problems

S. Gratton; Philippe Toint; J. Tshimanga Ilunga

doi:10.1137/090780493

Range-space variants and inexact matrix-vector products in Krylov solvers for linear systems arising from inverse problems

S. Gratton, Philippe Toint, J. Tshimanga Ilunga

Résultats de recherche: Contribution à un journal/une revue › Article

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Résumé

The objects of this paper are to introduce range-space variants of standard Krylov iterative solvers for unsymmetric and symmetric linear systems and to discuss how inexact matrix-vector products may be used in this context. The new range-space variants are characterized by possibly much lower storage and computational costs than their full-space counterparts, which is crucial in data assimilation applications and other inverse problems. However, this gain is achieved without sacrificing the inherent monotonicity properties of the original algorithms, which are of paramount importance in data assimilation applications. The use of inexact matrix-vector products is shown to further reduce computational cost in a controlled manner. Formal error bounds are derived on the size of the residuals obtained under two different accuracy models, and it is shown why a model controlling forward error on the product result is often preferable to one controlling backward error on the operator. Simple numerical examples finally illustrate the developed concepts and methods.

langue originale	Anglais
Pages (de - à)	969-986
Nombre de pages	18
journal	SIAM Journal on Matrix Analysis and Applications
Volume	32
Numéro de publication	3
Les DOIs	https://doi.org/10.1137/090780493
état	Publié - 1 janv. 2011

Empreinte digitale

Cross product

Matrix Product

Inverse Problem

Data Assimilation

Linear Systems

Computational Cost

Range of data

Backward Error

Iterative Solvers

Error Bounds

Monotonicity

Numerical Examples

Operator

Model

Citer ceci

Gratton, S., Toint, P., & Tshimanga Ilunga, J. (2011). Range-space variants and inexact matrix-vector products in Krylov solvers for linear systems arising from inverse problems. SIAM Journal on Matrix Analysis and Applications, 32(3), 969-986. https://doi.org/10.1137/090780493

Gratton, S. ; Toint, Philippe ; Tshimanga Ilunga, J. / Range-space variants and inexact matrix-vector products in Krylov solvers for linear systems arising from inverse problems. Dans: SIAM Journal on Matrix Analysis and Applications. 2011 ; Vol 32, Numéro 3. p. 969-986.

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Gratton, S, Toint, P & Tshimanga Ilunga, J 2011, 'Range-space variants and inexact matrix-vector products in Krylov solvers for linear systems arising from inverse problems', SIAM Journal on Matrix Analysis and Applications, VOL. 32, Numéro 3, p. 969-986. https://doi.org/10.1137/090780493

Range-space variants and inexact matrix-vector products in Krylov solvers for linear systems arising from inverse problems. / Gratton, S.; Toint, Philippe; Tshimanga Ilunga, J.

Dans: SIAM Journal on Matrix Analysis and Applications, Vol 32, Numéro 3, 01.01.2011, p. 969-986.

Résultats de recherche: Contribution à un journal/une revue › Article

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