<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

Published Online: May 27, 2024

Page range: 105 - 126

Received: Dec 01, 2022

Accepted: Apr 20, 2023

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

Keywords
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

Published Online: May 27, 2024

Page range: 105 - 126

Received: Dec 01, 2022

Accepted: Apr 20, 2023

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

KeywordsNonsymmetric 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.

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