On Solving Pentadiagonal Linear Systems via Transformations

TL;DR

This paper introduces new numeric and symbolic algorithms for solving pentadiagonal linear systems using transformations, improving robustness and extending previous methods, with demonstrated effectiveness through MATLAB experiments.

Contribution

It presents novel symbolic algorithms that address failure cases of numeric methods for pentadiagonal systems, generalizing prior work.

Findings

Algorithms successfully solve pentadiagonal systems.

Symbolic algorithms handle cases where numeric methods fail.

Experiments confirm efficiency and robustness.

Abstract

Many authors studied numeric algorithms for solving the linear systems of the pentadiagonal type. The well-known Fast Pentadiagonal System Solver algorithm is an example of such algorithms. The current article are described new numeric and symbolic algorithms for solving pentadiagonal linear systems via transformations. New algorithms are natural generalization of the work presented in [Moawwad El- Mikkawy and Faiz Atlan, Algorithms for Solving Linear Systems of Equations of Tridiagonal Type via Transformations, Applied Mathematics, 2014, 5, 413-422]. The symbolic algorithms remove the cases where the numeric algorithms fail. The computational cost of our algorithms is given. Some examples are given in order to illustrate the effectiveness of the proposed algorithms. All of the experiments are performed on a computer with the aid of programs written in MATLAB.