Abstract
The WZ factorization suitable for parallel computing, was introduced by Evans. A block generalization of the ABS class of methods for the solution of linear system of equations is given and it is shown that it covers the whole class of conjugate direction methods dened by Stewart. The methods produce a factorization of the coecient matrix implicitly, generating well known matrix factorizations. Here, we show how to set the parameters of a block ABS algorithm to compute the WZ and ZW fac- torizations of a nonsingular matrix as well as the WTW and ZTZ factorizations of a symmetric positives denite matrix. We also show how to appropriate the pa- rameters to construct algorithms for computing the QZ and the QW factorizations, where QTQ is an X-matrix. We also provide a new interpretation of the necessary and sucient condition for the existence of the WZ and the ZW factorizations of a nonsingular matrix.
Highlights
IntroductionThe integer ABS (IABS) class of algorithms has been developed by Esmaeili et al [5, 6] to compute the general integer solution of linear Diophantine equations
The central problem of linear algebra is the solution of linear system of equations Ax = b
Implicit matrix elimination schemes for solving linear systems were introduced by Evans [8] and Evans and Hatzopoulos [7]
Summary
The integer ABS (IABS) class of algorithms has been developed by Esmaeili et al [5, 6] to compute the general integer solution of linear Diophantine equations. Define Vi+1 ∈ Rn×ni+1 , an arbitrary full column rank matrix with column being linearly independent of columns of V1, · · · , Vi. One main result of the ABS algorithms has been the derivation of the ABS class of algorithms for linear Diophantine equations given by Esmaeili, MahdaviAmiri and Spedicato [6] and its extension using the scaled ABS algorithms [21].
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Statistics, Optimization & Information Computing
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
