PARALLEL INTERVAL MATRIX MULTISPLITTING AOR METHODS AND THEIR CONVERGENCE

This paper proposes a class of parallel interval matrix multisplitting AOR methods far solving systems of interval linear equations and discusses their convergence properties under the conditions that the coefficient matrices are interval H-matrices.

ON THE CONVERGENCE OF ASYNCHRONOUS NESTEDMATRIX MULTISPLITTING METHODS FOR LINEARSYSTEMS

A class of asynchronous nested matrix multisplitting methods for solving large-scale systems of linear equations are proposed, and their convergence characterizations are studied in detail when the coefficient matrices of the linear systems are monotone matrices and H-matrices, respectively.

ON THE CONVERGENCE DOMAIN OF THE MATRIX MULTISPLITTING RELAXATION METHODS FOR LINEAR SYSTEMS

The convergence of the parallel matrix multisplitting relaxation methods presented by Wang (Linear Algebra and Its Applications 154/156 (1991) 473 486) is further investigated. The investigations show that these relaxation methods really have considerably larger convergence domains.

A CLASS OF GENERALIZED MULTISPLITTING RELAXATION METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS

Abstract In this paper,a class of generalized parallel matrix multisplitting relaxation methods for solving linear complementarity problems on the high speed multiprocessor systems is set up.This class of methods not only includes all the existing relaxation methods for the linear complementarity problems,but also yields a lot of novel ones in the sense of multisplitting.We establish the convergence theories of this class of generalized parallel multisplitting relaxation methods under the condition that the system matrix is an H matrix with positive diagonal elements.

A CLASS OF ASYNCHRONOUS PARALLEL MULTISPLITTING RELAXATION METHODS FOR LARGE SPARSE LINEAR COMPLEMENTARITY PROBLEMS

Asynchronous parallel multisplitting relaxation methods for solving large sparse linear complementarity problems are presented, and their convergence is proved when the system matrices are H-matrices having positive diagonal elements. Moreover, block and multi-parameter variants of the new methods, together with their convergence properties, are investigated in detail. Numerical results show that these new methods can achieve high parallel efficiency for solving the large sparse linear complementarity problems on multiprocessor systems.

PARALLEL CHAOTIC MULTISPLITTING ITERATIVE METHODS FOR THE LARGE SPARSE LINEAR COMPLEMENTARITY PROBLEM

Focuses on a study which presented a parallel chaotic multisplitting method for solving the large sparse linear complementarity problem. Preliminaries of the study; Equations of the parallel chaotic multisplitting method; Information on the convergence theories; Details on the parallel chaotic multisplitting relaxation methods.

A CLASS OF ASYNCHRONOUS MATRIX MULTI-SPLITTING MULTI-PARAMETER RELAXATION ITERATIONS

A class of asynchronous matrix multi-splitting multi-parameter relaxation methods, including the asynchronous matrix multisplitting SAOR, SSOR and SGS methods as well. as the known asynchronous matrix multisplitting AOR, SOR and GS methods, etc., is proposed for solving the large sparse systems of linear equations by making use of the principle of sufficiently using the delayed information. These new methods can greatly execute the parallel computational efficiency of the MIMD-systems, and are shown to be convergent when the coefficient matrices are H-matrices. Moreover, necessary and sufficient conditions ensuring the convergence of these methods are concluded for the case that the coefficient matrices are L-matrices.

EXPERIMENTAL STUDY OF THE ASYNCHRONOUS MULTISPLITTING RELAXATION METHODS FOR THE LINEAR COMPLEMENTARITY PROBLEMS

Presents a study of the numerical behaviors of the relaxed asynchronous multisplitting methods for linear complementarity problems by solving typical problems from practical applications on a real multiprocessor system. Description of the tested problems and computing environment used in the computations; Description of the asynchronous multisplitting unsymmetric accelerated overrelaxation method; Discussion of results.

RELAXED ASYNCHRONOUS ITERATIONS FOR THE LINEAR COMPLEMENTARITY PROBLEM

Presents a class of relaxed asynchronous parallel multisplitting iterative methods for solving the linear complementarity problem on multiprocessor systems. Establishment of the methods; Convergence theories; Numerical results.