Computing the Pseudoinverse of Specific Toeplitz Matrices Using Rank-One Updates

Abstract

Application of the pure rank-one update algorithm as well as a combination of rank-one updates and the Sherman-Morrison formula in computing the Moore-Penrose inverse of the particular Toeplitz matrix is investigated in the present paper. Such Toeplitz matrices appear in the image restoration process and in many scientific areas that use the convolution. Four different approaches are developed, implemented, and tested on a number of numerical experiments.