On Solving Block Toeplitz Systems Using a Block Schur Algorithm

Abstract

This paper presents a block Schur algorithm to obtain a factorization of a symmetric block Toeplitz matrix. We develop a version based on block hyperbolic Householder reflectors by adapting the representation schemes for block Householder reflectors to the hyperbolic case. If a singular principal submatrix is encountered during the factorization, the matrix is perturbed and an approximate factorization is obtained. This is then combined with iterative refinement to obtain the final solution.