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dc.contributor.authorPestana, Jennifer
dc.contributor.authorWathen, Andrew J.
dc.date.accessioned2016-02-25T13:44:28Z
dc.date.available2016-02-25T13:44:28Z
dc.date.issued2015-01
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.
dc.identifier.issn0036-1445
dc.identifier.issn1095-7200
dc.identifier.doi10.1137/130934921
dc.identifier.urihttp://hdl.handle.net/10754/598959
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.
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).
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)
dc.subjectInf-sup constant
dc.subjectIterative solvers
dc.subjectPreconditioning
dc.subjectSaddle point problems
dc.titleNatural Preconditioning and Iterative Methods for Saddle Point Systems
dc.typeArticle
dc.identifier.journalSIAM Review
dc.contributor.institutionUniversity of Manchester, Manchester, United Kingdom
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdom
kaust.grant.numberKUK-C1-013-04


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