Quasiseparable Representations: The Basics

Abstract

Here we consider diagonal plus semiseparable representations of matrices. This is a direct generalization of diagonal plus separable representations studied in Chapter 1. Note that every matrix may be represented in the diagonal plus semiseparable form. The problem is to obtain such a representation with minimal orders. This may be treated as the problem of completing strictly lower triangular and strictly upper triangular parts of a matrix to matrices with minimal ranks, since it will be proved that minimal orders of the generators are equal to the ranks of those minimal completions. Thus one can apply results of Chapter 2 to determine diagonal plus semiseparable representation of a matrix. An algorithm for finding minimal generators of a semiseparable representation of a given matrix is presented.