A preconditioning strategy for banded circulant and toeplitz systems

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