Efficient Algorithm for Computing Inverse of Parametric Matrices

Abstract

In this paper, we study and compute the inverse of matrices with parametric entries. We demonstrate that the Gauss-Jordan method can be extended to compute the inverse of parametric matrices, offering a powerful tool for solving systems of linear equations and analyzing parametric systems. Using this new expansion (so-called Gauss-Jordan systems) and also utilizing linearly dependency systems for linear systems involving parameters [4, 5], we introduce the notion of an inverse matrix system for a parametric matrix. In doing so, we decompose the space of parameters into a finite partition and for each partition, we give the corresponding inverse matrix without applying Gröbner systems. We also present an algorithm for computing an inverse system for a given parametric matrix. All mentioned algorithms have been implemented in Maple, and their efficiency and behavior have been experimented on a set of benchmark matrices.