Natural Preconditioning and Iterative Methods for Saddle Point Systems

Handle URI:
http://hdl.handle.net/10754/598959
Title:
Natural Preconditioning and Iterative Methods for Saddle Point Systems
Authors:
Pestana, Jennifer; Wathen, Andrew J.
Abstract:
© 2015 Society for Industrial and Applied Mathematics. The solution of quadratic or locally quadratic extremum problems subject to linear(ized) constraints gives rise to linear systems in saddle point form. This is true whether in the continuous or the discrete setting, so saddle point systems arising from the discretization of partial differential equation problems, such as those describing electromagnetic problems or incompressible flow, lead to equations with this structure, as do, for example, interior point methods and the sequential quadratic programming approach to nonlinear optimization. This survey concerns iterative solution methods for these problems and, in particular, shows how the problem formulation leads to natural preconditioners which guarantee a fast rate of convergence of the relevant iterative methods. These preconditioners are related to the original extremum problem and their effectiveness - in terms of rapidity of convergence - is established here via a proof of general bounds on the eigenvalues of the preconditioned saddle point matrix on which iteration convergence depends.
Citation:
Pestana J, Wathen AJ (2015) Natural Preconditioning and Iterative Methods for Saddle Point Systems. SIAM Review 57: 71–91. Available: http://dx.doi.org/10.1137/130934921.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Review
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2015
DOI:
10.1137/130934921
Type:
Article
ISSN:
0036-1445; 1095-7200
Sponsors:
This publication was based on work supported in part by award KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorPestana, Jenniferen
dc.contributor.authorWathen, Andrew J.en
dc.date.accessioned2016-02-25T13:44:28Zen
dc.date.available2016-02-25T13:44:28Zen
dc.date.issued2015-01en
dc.identifier.citationPestana J, Wathen AJ (2015) Natural Preconditioning and Iterative Methods for Saddle Point Systems. SIAM Review 57: 71–91. Available: http://dx.doi.org/10.1137/130934921.en
dc.identifier.issn0036-1445en
dc.identifier.issn1095-7200en
dc.identifier.doi10.1137/130934921en
dc.identifier.urihttp://hdl.handle.net/10754/598959en
dc.description.abstract© 2015 Society for Industrial and Applied Mathematics. The solution of quadratic or locally quadratic extremum problems subject to linear(ized) constraints gives rise to linear systems in saddle point form. This is true whether in the continuous or the discrete setting, so saddle point systems arising from the discretization of partial differential equation problems, such as those describing electromagnetic problems or incompressible flow, lead to equations with this structure, as do, for example, interior point methods and the sequential quadratic programming approach to nonlinear optimization. This survey concerns iterative solution methods for these problems and, in particular, shows how the problem formulation leads to natural preconditioners which guarantee a fast rate of convergence of the relevant iterative methods. These preconditioners are related to the original extremum problem and their effectiveness - in terms of rapidity of convergence - is established here via a proof of general bounds on the eigenvalues of the preconditioned saddle point matrix on which iteration convergence depends.en
dc.description.sponsorshipThis publication was based on work supported in part by award KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectInf-sup constanten
dc.subjectIterative solversen
dc.subjectPreconditioningen
dc.subjectSaddle point problemsen
dc.titleNatural Preconditioning and Iterative Methods for Saddle Point Systemsen
dc.typeArticleen
dc.identifier.journalSIAM Reviewen
dc.contributor.institutionUniversity of Manchester, Manchester, United Kingdomen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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