Optimized Cramer’s Rule in WZ Factorization and Applications

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.

A Review on Quadrant Interlocking Factorization: WZ and WH Factorization

“…(n − 2k) of 2 × 2 linear systems to be solved which account for the elements in W -matrix and Z-matrix [17]. The direct method to solve the linear systems of QIF under the nonsingularity constraint presumed for their determinants solely depends on a conventional method called Cramer's rule.…”