## Andrew Knyazev (Mitsubishi Electric Research Laboratories)-Absolute Value Preconditioning for Symmetric Indefinite Linear Systems

Mathematics - Colloquium

Friday, March 1, 2013

11:00 AM-12:00 PM

Stratton Hall

203

ABSTRACT: We introduce a novel strategy, absolute value preconditioning, for constructing symmetric positive definite (SPD preconditioners for linear systems with symmetric indefinite matrices. We consider a model problem with a shifted discrete negative Laplacian, and suggest a geometric multigrid (MG) preconditioner, where the inverse of the matrix absolute value appears only on the coarse grid, while operations on finer grids are based on the Laplacian. Our numerical tests demonstrate practical effectiveness of the new preconditioner.

[http://arxiv.org/abs/1104.4530]

Suggested Audiences:
Adult, College

E-mail:
ma-chair@wpi.edu

Last Modified: February 15, 2013 at 4:53 PM

## Andrew Knyazev (Mitsubishi Electric Research Laboratories)-Absolute Value Preconditioning for Symmetric Indefinite Linear Systems

Mathematics - Colloquium

Friday, March 1, 2013

11:00 AM-12:00 PM

Stratton Hall

203

ABSTRACT: We introduce a novel strategy, absolute value preconditioning, for constructing symmetric positive definite (SPD preconditioners for linear systems with symmetric indefinite matrices. We consider a model problem with a shifted discrete negative Laplacian, and suggest a geometric multigrid (MG) preconditioner, where the inverse of the matrix absolute value appears only on the coarse grid, while operations on finer grids are based on the Laplacian. Our numerical tests demonstrate practical effectiveness of the new preconditioner.

[http://arxiv.org/abs/1104.4530]

Suggested Audiences: Adult, College

E-mail: ma-chair@wpi.edu

Last Modified: February 15, 2013 at 4:53 PM