<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>An approximate inverse <italic>LU</italic> preconditioner is constructed based on the Sherman–Morrison formula. Applying recursively that inversion formula a multiplicative decomposition of the inverse of a matrix is obtained. This recursion in compact form is the base to build the proposed preconditioner that we call V–AISM. For nonsingular <italic>M</italic>-matrices and <italic>H</italic>-matrices of the invertible class the stability of the preconditioner is proved. Numerical results show that V–AISM is robust and competitive compared with other preconditioners.</p>
</abstract>

An approximate inverse LU preconditioner is constructed based on the Sherman–Morrison formula. Applying recursively that inversion formula a multiplicative decomposition of the inverse of a matrix is obtained. This recursion in compact form is the base to build the proposed preconditioner that we call V–AISM. For nonsingular M-matrices and H-matrices of the invertible class the stability of the preconditioner is proved. Numerical results show that V–AISM is robust and competitive compared with other preconditioners.

An inverse LU preconditioner based on the Sherman–Morrison formula

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"An inverse LU preconditioner based on the Sherman\u2013Morrison formula"}

An approximate inverse LU preconditioner is constructed based on the Sherman–Morrison formula. Applying recursively that inversion formula a multiplicative...

An inverse LU preconditioner based on the Sherman–Morrison formula

Publié en ligne: 27 mai 2024

Pages: 105 - 126

Reçu: 01 déc. 2022

Accepté: 20 avr. 2023

DOI: https://doi.org/10.2478/auom-2024-0006

Mots clés
Nonsymmetric linear systems, iterative methods, aproximate inverse preconditioning, Sherman-Morrison formula

© 2024 R. Bru, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

An inverse LU preconditioner based on the Sherman–Morrison formula

Publié en ligne: 27 mai 2024

Pages: 105 - 126

Reçu: 01 déc. 2022

Accepté: 20 avr. 2023

DOI: https://doi.org/10.2478/auom-2024-0006

Mots clésNonsymmetric linear systems, iterative methods, aproximate inverse preconditioning, Sherman-Morrison formula

© 2024 R. Bru, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
Nonsymmetric linear systems, iterative methods, aproximate inverse preconditioning, Sherman-Morrison formula