On solving block Toeplitz matrices using a block Schur algorithm
Kyle A. Gallivan, S. Thirumalai, Paul Van Dooren · Digital Access to Libraries (Université catholique de Louvain (UCL), l'Université de Namur (UNamur) and the Université Saint-Louis (USL-B)) · 1994
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.