Optimized Cramer’s Rule in WZ Factorization and Applications

Authors

  • Olayiwola Babarinsa Faculty of Bioengineering & Technology, Universiti Malaysia Kelantan, 16100 Kota Bharu, Kelantan, Malaysia https://orcid.org/0000-0002-3569-0828
  • Azfi Zaidi Mohammad Sofi Faculty of Bioengineering $\&$ Technology, Universiti Malaysia Kelantan, 16100 Kota Bharu, Kelantan, Malaysia
  • Mohd Asrul Hery Ibrahim Faculty of Bioengineering $\&$ Technology, Universiti Malaysia Kelantan, 16100 Kota Bharu, Kelantan, Malaysia https://orcid.org/0000-0002-6950-6937
  • Hailiz Kamarulhaili School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia https://orcid.org/0000-0003-4309-4804

DOI:

https://doi.org/10.29020/nybg.ejpam.v13i4.3818

Keywords:

WZ factorization, LU factorization, Linear systems, Cramer’s rule, MATLAB

Abstract

In this paper, W Z factorization is optimized with a proposed Cramer’s rule and compared with classical Cramer’s rule to solve the linear systems of the factorization technique. The matrix norms and performance time of WZ factorization together with LU factorization are analyzed using sparse matrices on MATLAB via AMD and Intel processor to deduce that the optimized Cramer’s rule in the factorization algorithm yields accurate results than LU factorization and conventional W Z factorization. In all, the matrix group and Schur complement for every Zsystem (2×2 block triangular matrices from Z-matrix) are established.

Author Biographies

  • Olayiwola Babarinsa, Faculty of Bioengineering & Technology, Universiti Malaysia Kelantan, 16100 Kota Bharu, Kelantan, Malaysia
    Postdoctoral researcher
  • Azfi Zaidi Mohammad Sofi, Faculty of Bioengineering $\&$ Technology, Universiti Malaysia Kelantan, 16100 Kota Bharu, Kelantan, Malaysia
    Associate professor
  • Mohd Asrul Hery Ibrahim, Faculty of Bioengineering $\&$ Technology, Universiti Malaysia Kelantan, 16100 Kota Bharu, Kelantan, Malaysia
    Lecturer
  • Hailiz Kamarulhaili, School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
    Professor and dean, school of mathematical sciences

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Published

2020-10-31

Issue

Section

Nonlinear Analysis

How to Cite

Optimized Cramer’s Rule in WZ Factorization and Applications. (2020). European Journal of Pure and Applied Mathematics, 13(4), 1035-1054. https://doi.org/10.29020/nybg.ejpam.v13i4.3818