On the Inverting of A General Heptadiagonal Matrix

TL;DR

This paper introduces efficient numeric and symbolic algorithms for inverting any nonsingular heptadiagonal matrix, ensuring stability and broad applicability without restrictive conditions, with computational cost proportional to matrix size.

Contribution

The paper presents new algorithms for inverting nonsingular heptadiagonal matrices that are both numerically stable and symbolic, with linear computational complexity and no restrictive assumptions.

Findings

Algorithms are efficient and suitable for computer algebra systems.

Symbolic algorithm remains stable without restrictive conditions.

Computational cost is linear in matrix size.

Abstract

In this paper, we developed new numeric and symbolic algorithms to find the inverse of any nonsingular heptadiagonal matrix. Symbolic algorithm will not break and it is without setting any restrictive conditions. The computational cost of our algorithms is $O(n)$. The algorithms are suitable for implementation using computer algebra system such as MAPLE, MATLAB and MATHEMATICA. Examples are given to illustrate the efficiency of the algorithms.