Scientific Annals of Computer Science (Jun 2024)
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.
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