Symbolic computation of weighted Moore-Penrose inverse using partitioning method

TL;DR

This paper introduces new algorithms for computing the weighted Moore-Penrose inverse of rational and polynomial matrices using a partitioning method, extending previous approaches for constant matrices.

Contribution

It generalizes existing methods to rational and polynomial matrices and provides algorithms implemented in MATHEMATICA for symbolic computation.

Findings

Algorithms successfully compute weighted Moore-Penrose inverse for rational matrices.

Algorithms extend to polynomial matrices with symbolic computation.

Implementation in MATHEMATICA demonstrates practical applicability.

Abstract

We propose a method and algorithm for computing the weighted Moore-Penrose inverse of one-variable rational matrices. Continuing this idea, we develop an algorithm for computing the weighted Moore-Penrose inverse of one-variable polynomial matrix. These methods and algorithms are generalizations of the method for computing the weighted Moore-Penrose inverse for constant matrices, originated in Wang and Chen [G.R. Wang, Y.L. Chen, A recursive algorithm for computing the weighted Moore-Penrose inverse AMN, J. Comput. Math. 4 (1986) 74-85], and the partitioning method for computing the Moore-Penrose inverse of rational and polynomial matrices introduced in Stanimirovic and Tasic [P.S. Stanimirovic, M.B. Tasic, Partitioning method for rational and polynomial matrices, Appl. Math. Comput. 155 (2004) 137-163]. Algorithms are implemented in the symbolic computational package MATHEMATICA.