Generalized inverses of Hankel and Toeplitz mosaic matrices

AbstractHankel and Toeplitz mosaic matrices are block matrices with Hankel or Toeplitz blocks, respectively. It is shown that Hankel and Toeplitz mosaic matrices possess reflexive generalized inverses which are Bezoutians. Furthermore the Bezoutian structure of the Moore-Penrose and group inverses is investigated

Generalized inversion of finite rank Hankel and Toeplitz operators with rational matrix symbols

AbstractThe goal of the paper is a generalized inversion of finite rank Hankel operators and Hankel or Toeplitz operators with block matrices having finitely many rows. To attain it a left coprime fractional factorization of a strictly proper rational matrix function and the Bezout equation are used. Generalized inverses of these operators and generating functions for the inverses are explicitly constructed in terms of the fractional factorization

Fast Algorithms for Displacement and Low-Rank Structured Matrices

This tutorial provides an introduction to the development of fast matrix algorithms based on the notions of displacement and various low-rank structures