International Journal For Multidisciplinary Research

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Comparative Mathematical Analysis of Gauss Jordan Elimination and Lu Decomposition

Author(s) Ms. S Yoga, B. Kanimozhi
Country India
Abstract Gauss Jordan elimination and LU decomposition serve as core numerical techniques for solving linear systems AX=b, delivering, identical solutions for square, non-singular matrices of any dimensions, including 4*4 ,5*5,and systems arising from nth degree polynomial interpolation via vandermonde matrices. Gauss Jordan transforms the augmented matrix to reduced row echelon form for direct solution readout, where as LU factorization A=LU employs forward substitution on LY=b followed by backward substitution on UX=Y. Empirical testes confirm equivalence across matrix sizes and polynomial contexts, rooted in shared Gaussian elimination foundations that preserve solution sets under exact arithmetic. Both excel in engineering, optimization and curve fitting, with LU offering superior efficiency for multiple right-hand sides through O (n2) substitution post factorization.
Keywords Jordan method, LU decomposition, Linear system, 4*4 matrix, 5*5 matrix, matrix factorization.
Field Mathematics
Published In Volume 8, Issue 2, March-April 2026
Published On 2026-03-19
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E-ISSN 2582-2160
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