The textit{QIF}  (Quadrant Interlocking Factorization) method of Evans and Hatzopoulos solves linear equation systems using textit{WZ}  factorization. The  WZ factorization can be faster than the textit{LU} factorization  because,  it performs the simultaneous evaluation of two columns or two rows. Here, we present a  method for computing the real and integer textit{WZ} and  textit{ZW} factoriz...

classes of‎ ‎abaffy-broyden-spedicato (abs) methods have been introduced for‎ ‎solving linear systems of equations‎. ‎the algorithms are powerful methods for developing matrix‎ ‎factorizations and many fundamental numerical linear algebra processes‎. ‎here‎, ‎we show how to apply the abs algorithms to devise algorithms to compute the wz and zw‎ ‎factorizations of a nonsingular matrix as well as...

classes of‎ ‎abaffy-broyden-spedicato (abs) methods have been introduced for‎ ‎solving linear systems of equations‎. ‎the algorithms are powerful methods for developing matrix‎ ‎factorizations and many fundamental numerical linear algebra processes‎. ‎here‎, ‎we show how to apply the abs algorithms to devise algorithms to compute the wz and zw‎ ‎factorizations of a nonsingular matrix as well as...

The WZ factorization for the solution of symmetric positive definite banded linear systems when combined with a partitioned scheme, renders a divide and conquer algorithm. The WZ factorization of the coefficient matrix in each block has the properties: the vector [a1, . . . , aβ , 0, . . . , 0, an−β+1, . . . , an] is invariant under the transformation W where β is the semibandwidth of the coeff...

Classes of‎ ‎Abaffy-Broyden-Spedicato (ABS) methods have been introduced for‎ ‎solving linear systems of equations‎. ‎The algorithms are powerful methods for developing matrix‎ ‎factorizations and many fundamental numerical linear algebra processes‎. ‎Here‎, ‎we show how to apply the ABS algorithms to devise algorithms to compute the WZ and ZW‎ ‎factorizations of a nonsingular matrix as well as...

Quadrant Interlocking Factorization (QIF), an alternative to LU factorization, is suitable for factorizing invertible matrix A such that det(A) , 0. The QIF, with its application in parallel computing, the most efficient factorization technique yet underutilized. two forms of QIF among others, which are not only similar algorithm but also computation, WZ and WH differs applications properties. ...

Abstract In the paper we present a vectorized algorithm for WZ factorization of a matrix which was implemented with the BLAS1 library. We present the results of numerical experiments which show that vectorization accelerates the sequential WZ factorization. Next, we parallelized both algorithms for a two-processor shared memory machine using the OpenMP standard. We present performances of these...

In this paper the authors present problems which can appear when a sparse square matrix (without any special structure) is factorized to a product of matrices W and Z. The fill-in problem is considered, and the manners of its solving – by permuting both rows and columns with a modified Markowitz scheme among others. The results of numerical experiments for sparse matrices of various sizes are p...