A note on superoptimal generalized circulant preconditioners

Authors:
Silvia Noschese;Lothar Reichel
Affiliations:
Dipartimento di Matematica "Guido Castelnuovo", Sapienza Universití di Roma, P.le A. Moro, 2, I-00185 Roma, Italy;Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA
Venue:
Applied Numerical Mathematics
Year:
2014

Citing 8
Cited 0

A proposal for toeplitz matrix calculations

Studies in Applied Mathematics
Optimal and superoptimal circulant preconditioners

SIAM Journal on Matrix Analysis and Applications
Circulant and skewcirculant matrices for solving Toeplitz matrix problems

SIAM Journal on Matrix Analysis and Applications
Some aspects of circulant preconditioners

SIAM Journal on Scientific Computing
Which circulant preconditioner is better?

Mathematics of Computation
Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems
Iterative Methods for Toeplitz Systems (Numerical Mathematics and Scientific Computation)

Iterative Methods for Toeplitz Systems (Numerical Mathematics and Scientific Computation)
An Introduction to Iterative Toeplitz Solvers (Fundamentals of Algorithms)

An Introduction to Iterative Toeplitz Solvers (Fundamentals of Algorithms)

Quantified Score

Hi-index	0.00

Visualization

Abstract

Circulant matrices can be effective preconditioners for linear systems of equations with a Toeplitz matrix. Several approaches to construct such preconditioners have been described in the literature. This paper focuses on the superoptimal circulant preconditioners proposed by Tyrtyshnikov, and investigates a generalization obtained by allowing generalized circulant matrices. Numerical examples illustrate that the new preconditioners so obtained can give faster convergence than available preconditioners based on circulant and generalized circulant matrices.