1994•International Journal of Computer MathematicsRequires access

A sparse preconditioner for symmetric positive definite banded circulant and toeplitz linear systems

David John Evans, Dušan Caf

Abstract

A tridiagonal circulant preconditioner for banded symmetric circulant linear systems which occur in digital signal processing (DSP) problems is studied. It is shown, that for banded symmetric positive definite (SPD) circulant matrices with bandwidth p and elements satisfying an efficient tridiagonal circulant preconditioner can be designed. The influence of a preconditioning parameter w on the condition number of the preconditioned linear system is studied and a formula for estimating is proposed.

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Key concepts: Circulant matrix, Toeplitz matrix, Preconditioner, Tridiagonal matrix, Mathematics, Positive-definite matrix, Linear system, Applied mathematics