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

Hakan Bagci, Joseph E. Pasciak, Kostyantyn Sirenko

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)371-392
Number of pages22
JournalNumerical Linear Algebra with Applications
Volume22
Issue number2
DOIs
StatePublished - Nov 11 2014

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

Fingerprint Dive into the research topics of 'A convergence analysis for a sweeping preconditioner for block tridiagonal systems of linear equations'. Together they form a unique fingerprint.

Cite this