Quadrant Interlocking Factorization Algorithm of Hourglass Matrix from Nonsingular Matrix

Abstract

This paper presents  the quadrant interlocking factorization ($QIF$) of nonsingular matrix, alternatively called $WH$ factorization, to yield  hourglass matrix ($H$-matrix). The $WH$ factorization algorithm of $H$-matrix is synonymous  to $WZ$ factorization algorithm of  $Z$-matrix, unlike  $LU$ factorization. We examine the conditions  to generate the zero and nonzero entries of $H$-matrix from the factorization algorithm, and  compare the $H$-matrix and $Z$-matrix. Then we conclude that the existence of  $WH$ factorization implies $WZ$ factorization.