ANALYTICAL SOLUTION OF LINEAR OPTIMIZATION PROBLEMS USING GAUSS ELIMINATION AND LU DECOMPOSITION METHODS
By
Rahidas Kumar1 and Manoranjan Kumar Singh2
1Department of Science & Humanities, R.V.S.C.E.T., Jamshedpur, Jharkhand, India-831012
2Professor and Head, Department of Mathematics, Magadh University, Bodh Gaya, Bihar, India-824234
Email: kumarahidas@gmail.com, drmksingh gaya@yahoo.com
(Received: October 09, 2023; In format: July 30, 2025; Received: November 25 , 2025; Accepted: December 02, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55225
Abstract
This paper presents a novel approach to address Linear Optimization Problems (LOPs) utilizing numerical analysis techniques, specifically the Gauss Elimination (GE) Method and LU Decomposition (LUD) Method for matrices. These methods centred on square matrices offer direct solutions without the need for iterative processes. The study demonstrates the superiority of these techniques over the Simplex Method.
2020 Mathematical Sciences Classification: 15A09, 15A23, 65F10, 65K10.
Keywords and Phrases: LOP, System of Linear Equations, GE, Upper Triangular Matrix, Augmented Matrix, LUD, Unit Lower Triangular Matrix, and Simplex Method.