Generalized Jacobi and Gauss-Seidel Method for Solving Non-Square Linear Systems

TL;DR

This paper extends Jacobi and Gauss-Seidel iterative methods to non-square linear systems, providing convergence conditions and a procedure to obtain solutions, with an example comparison.

Contribution

It introduces generalized iterative procedures for non-square systems and establishes convergence criteria, which is a novel extension of classical methods.

Findings

Derived sufficient convergence conditions for the new methods.

Provided a procedure to extract exact solutions from iterative approximations.

Compared the generalized methods with existing approaches through an example.

Abstract

The main goal of this paper is to generalize Jacobi and Gauss-Seidel methods for solving non-square linear system. Towards this goal, we present iterative procedures to obtain an approximate solution for non-square linear system. We derive sufficient conditions for the convergence of such iterative methods. Procedure is given to show that how an exact solution can be obtained from these methods. Lastly, an example is considered to compare these methods with other available method(s) for the same.