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Paper   IPM / M / 17651
School of Mathematics
  Title:   Efficient algorithm for computing inverse of parametric matrices
  Author(s):  Mahdi Dehghani Darmian
  Status:   Published
  Journal: Scientific Annals of "Alexandru Ioan Cuza" University of Iasi
  Year:  2024
  Pages:   DOI: 10.7561/SACS.2024.1.1
  Supported by:  IPM
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 Gr¨obner 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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