Reconfiguration based model for matrix triangulation and hardware device creation concept

Abstract

This research article based on the dynamic partial reconfiguration process gives a new orientation to the idea behind the matrix inverse computation method. The conventional way of computing matrix inverse uses the "Gauss's Methods" or any optimized variant of it. This research extends the classical method limited to the optimal "Gauss's Derivative Algorithms". The new algorithm based on the "Reconfiguration Concept" has been applied and provides matrix inverse without using "Gauss's Analysis". Instead, the computation idea will be based on the reconfigured "RLP". A wide range of $$n \times n$$n×n matrix computations have been tested for their feasibility and correctness. In this paper, we assume that such an algorithm exists that can compute the inverse matrices using the partial reconfiguration concept; we then use this idea to develop a reconfiguration-based model for matrix factorization and matrix reduction. Our reconfiguration model neither utilizes any standard algorithm to achieve the decomposition or the reduction nor any related matrix concept that factorizes matrices. However, it will use the reconfiguration matrix inverse computation to triangulate matrices. The model is described by a "Vector-Matrix Equation" reconfigured from the recursive dynamic process. Since the assumptions of our model are derived from the reconfiguration matrix inverse computations, it correctly computes the triangulated matrices. Another contribution of our work is the reduction of matrices into trivial identity matrices. Our model produces triangular matrices that avoid computational failures due to matrix inverse singularity conditions; thus,this matrix factorization management approach offers a new matrix-based computation standard.