Direct Solution Method for System of Linear Equations

TL;DR

This paper introduces a new direct method for solving large systems of linear equations that enhances numerical stability using orthogonal matrices, eliminating the need for special treatments.

Contribution

The paper proposes a novel direct solution method employing orthogonal matrices to improve numerical stability in large linear systems.

Findings

Method achieves stable solutions without special treatments

Applicable to large systems of equations

Reduces computational instability issues

Abstract

Direct solution of simultaneous linear equations is regarded to be slow for large systems of equations and requires special treatment to avoid numerical instability. A new method is proposed that addresses the numerical instability without any special treatments. The method uses the orthogonal matrices to achieve numerical stability.