On block matrices with elements of special structure

Abstract

In various signal processing applications one is often confronted with aspects such as linear system solution, triangularization or inversion of matrices with special block structure as well as entries of particular form. Toeplitz, Banded Toeplitz, circular and Hankel matrices provide typical examples often encountered in such diverse fields as image processing, computerized tomography and other array processing applications. The purpose of this paper is to algorithmically examine the issues of triangularization, inversion and linear system solution when the above particular structures are imposed at either the block level or the entry level. It is shown that the various resulting combinations of block and entry structure considerably reduce the computational complexity of the above problems.