A preconditioning strategy for banded circulant and toeplitz systems

Abstract

A new preconditioning strategy for symmetric positive definite banded circulant and Toeplitz systems is described. The optimal tridiagonal preconditioner for tridiagonal circulant systems is modified and applied to both circulant and Toeplitz banded systems. The strategy is extended to block tridiagonal systems. The parallelisation aspects of the PCG algorithm are discussed.

Keywords:

• Optimal preconditioner
• banded Circulant/Toeplitz systems
• PCG algorithm

C.R. Categories:

• G.1.3

^∗Corresponding author. Now at Management Information Service Chamber of Commerce and Industry of Slovenia Slovenska Cesta 41 S1- 1504 Ljubijana, Slovenia.

^†Dept of Computing, Nottingham Trent University, Nottingham U.K.

^∗Corresponding author. Now at Management Information Service Chamber of Commerce and Industry of Slovenia Slovenska Cesta 41 S1- 1504 Ljubijana, Slovenia.

^†Dept of Computing, Nottingham Trent University, Nottingham U.K.

Notes

^∗Corresponding author. Now at Management Information Service Chamber of Commerce and Industry of Slovenia Slovenska Cesta 41 S1- 1504 Ljubijana, Slovenia.

^†Dept of Computing, Nottingham Trent University, Nottingham U.K.