Effective partitioning method for computing weighted Moore-Penrose inverse

TL;DR

This paper presents a new partitioning algorithm for efficiently computing the weighted Moore-Penrose inverse of multi-variable polynomial matrices, especially optimized for sparse matrices, with implementations in MATHEMATICA.

Contribution

It generalizes existing algorithms to handle multi-variable rational and polynomial matrices and improves performance for sparse matrices.

Findings

Algorithm successfully computes weighted Moore-Penrose inverse for complex matrices.

Implementation in MATHEMATICA demonstrates practical efficiency.

Method extends previous partitioning techniques to broader matrix classes.

Abstract

We introduce a method and an algorithm for computing the weighted Moore-Penrose inverse of multiple-variable polynomial matrix and the related algorithm which is appropriated for sparse polynomial matrices. These methods and algorithms are generalizations of algorithms developed in [M.B. Tasic, P.S. Stanimirovic, M.D. Petkovic, Symbolic computation of weighted Moore-Penrose inverse using partitioning method, Appl. Math. Comput. 189 (2007) 615-640] to multiple-variable rational and polynomial matrices and improvements of these algorithms on sparse matrices. Also, these methods are generalizations of the partitioning method for computing the Moore-Penrose inverse of rational and polynomial matrices introduced in [P.S. Stanimirovic, M.B. Tasic, Partitioning method for rational and polynomial matrices, Appl. Math. Comput. 155 (2004) 137-163; M.D. Petkovic, P.S. Stanimirovic, Symbolic computation of the Moore-Penrose inverse using partitioning method, Internat. J. Comput. Math. 82 (2005) 355-367] to the case of weighted Moore-Penrose inverse. Algorithms are implemented in the symbolic computational package MATHEMATICA.