<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Updating preconditioners for the solution of sequences of large and sparse saddle- point linear systems via Krylov methods has received increasing attention in the last few years, because it allows to reduce the cost of preconditioning while keeping the efficiency of the overall solution process. This paper provides a short survey of the two approaches proposed in the literature for this problem: updating the factors of a preconditioner available in a block LDL<sup>T</sup> form, and updating a preconditioner via a limited-memory technique inspired by quasi-Newton methods.</p></abstract>

Updating preconditioners for the solution of sequences of large and sparse saddle- point linear systems via Krylov methods has received increasing attention in the last few years, because it allows to reduce the cost of preconditioning while keeping the efficiency of the overall solution process. This paper provides a short survey of the two approaches proposed in the literature for this problem: updating the factors of a preconditioner available in a block LDLT form, and updating a preconditioner via a limited-memory technique inspired by quasi-Newton methods.

On preconditioner updates for sequences of saddle-point linear systems

Communications in Applied and Industrial Mathematics

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

{"article-title":"On preconditioner updates for sequences of saddle-point linear systems"}

Updating preconditioners for the solution of sequences of large and sparse saddle- point linear systems via Krylov methods has received increasing attention in...

On preconditioner updates for sequences of saddle-point linear systems

Published Online: Feb 28, 2018

Page range: 35 - 41

Received: Oct 17, 2017

Accepted: Dec 04, 2017

DOI: https://doi.org/10.1515/caim-2018-0003

Keywords
saddle-point matrices, sequences of linear systems, preconditioning, factorization updates, limited-memory techniques

© 2018

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

On preconditioner updates for sequences of saddle-point linear systems

Published Online: Feb 28, 2018

Page range: 35 - 41

Received: Oct 17, 2017

Accepted: Dec 04, 2017

DOI: https://doi.org/10.1515/caim-2018-0003

Keywordssaddle-point matrices, sequences of linear systems, preconditioning, factorization updates, limited-memory techniques

© 2018

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

Keywords
saddle-point matrices, sequences of linear systems, preconditioning, factorization updates, limited-memory techniques