A convergence analysis for a sweeping preconditioner for block tridiagonal systems of linear equations

Handle URI:
http://hdl.handle.net/10754/563852
Title:
A convergence analysis for a sweeping preconditioner for block tridiagonal systems of linear equations
Authors:
Bagci, Hakan ( 0000-0003-3867-5786 ) ; Pasciak, Joseph E.; Sirenko, Kostyantyn
Abstract:
We study sweeping preconditioners for symmetric and positive definite block tridiagonal systems of linear equations. The algorithm provides an approximate inverse that can be used directly or in a preconditioned iterative scheme. These algorithms are based on replacing the Schur complements appearing in a block Gaussian elimination direct solve by hierarchical matrix approximations with reduced off-diagonal ranks. This involves developing low rank hierarchical approximations to inverses. We first provide a convergence analysis for the algorithm for reduced rank hierarchical inverse approximation. These results are then used to prove convergence and preconditioning estimates for the resulting sweeping preconditioner.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Electrical Engineering Program; Computational Electromagnetics Laboratory
Publisher:
Wiley-Blackwell
Journal:
Numerical Linear Algebra with Applications
Issue Date:
11-Nov-2014
DOI:
10.1002/nla.1961
Type:
Article
ISSN:
10705325
Sponsors:
This work was supported in part by the National Science Foundation through grant DMS-0609544. It was also supported in part by award number KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Articles; Electrical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBagci, Hakanen
dc.contributor.authorPasciak, Joseph E.en
dc.contributor.authorSirenko, Kostyantynen
dc.date.accessioned2015-08-03T12:16:58Zen
dc.date.available2015-08-03T12:16:58Zen
dc.date.issued2014-11-11en
dc.identifier.issn10705325en
dc.identifier.doi10.1002/nla.1961en
dc.identifier.urihttp://hdl.handle.net/10754/563852en
dc.description.abstractWe study sweeping preconditioners for symmetric and positive definite block tridiagonal systems of linear equations. The algorithm provides an approximate inverse that can be used directly or in a preconditioned iterative scheme. These algorithms are based on replacing the Schur complements appearing in a block Gaussian elimination direct solve by hierarchical matrix approximations with reduced off-diagonal ranks. This involves developing low rank hierarchical approximations to inverses. We first provide a convergence analysis for the algorithm for reduced rank hierarchical inverse approximation. These results are then used to prove convergence and preconditioning estimates for the resulting sweeping preconditioner.en
dc.description.sponsorshipThis work was supported in part by the National Science Foundation through grant DMS-0609544. It was also supported in part by award number KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherWiley-Blackwellen
dc.subjectCartesian PMLen
dc.subjectHelmholtz equationen
dc.subjectPerfectly matched layeren
dc.subjectSweeping preconditioneren
dc.titleA convergence analysis for a sweeping preconditioner for block tridiagonal systems of linear equationsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentElectrical Engineering Programen
dc.contributor.departmentComputational Electromagnetics Laboratoryen
dc.identifier.journalNumerical Linear Algebra with Applicationsen
dc.contributor.institutionDepartment of Mathematics, Texas A and M UniversityCollege Station, TX, United Statesen
kaust.authorBagci, Hakanen
kaust.authorSirenko, Kostyantynen
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