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.

ASYNCHRONOUS RELAXED ITERATIVE METHODS FOR SOLVING LINEAR SYSTEMS OF EQUATIONS

In this paper, the asynchronous versions of classical iterative methods for solving linear systems of equations are considered. Sufficient conditions for convergence of asynchronous relaxed processes are given for H-matrix by which nor only the requirements of [3] on coefficient matrix are lowered, but also a larger region of convergence than that in [3] is obtained.

MODELS OF ASYNCHRONOUS MRALLEL NONLINEAR MULTISPLITTING RELAXED ITERATIONS

In the sense of the nonlinear multisplitting and based on the principle of suffi-ciently using the delayed information, we propose models of asynchronous parallelaccelerated overrelaxation iteration methods for solving large scale system of non-linear equations. Under proper conditions, we set up the local convergence theoriesof these new method models.

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.

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.

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.

A NEW GENERALIZED ASYNCHRONOUS PARALLELMULTISPLITTING ITERATION METHOD

For the large sparse systems of linear and nonlinear equations, a new class of generalized asynchronous parallel multisplitting iterative method is presented, and its convergence theory is established under suitable conditions. This method not only unifies the discussions of various existing asynchronous multisplitting iterations, but also affords new algorithmic and theoretical results for the parallel solution of large sparse system of linear equations. Besides its generality, this method is also much more suitable for implementing on the MIMD multiprocessor systems.

NonlinearAsynchronousBlockIterativeMethod

This paper proposes a class of asynchronous block iterative methods for solving large scale nonlinear equations F(x)=0 and proves local convergence. This method splits F into p blocks, then does the asynchronous parallel iteration on the p multiprocessor with shared memory. Because each processor need only solve equations with a low dimension and there is no synchronous waiting time, the parallel efficiency can be increased. Finally, we give the results of the numerical test of three kinds of Newton like asynchronous block iteration methods which run well on a multiprocessor system. These results show that the parallel efficiency is very high.

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.

Multisplitting Iteration Schemes for Solving a Class of Nonlinear Complementarity Problems

We consider several synchronous and asynchronous multisplitting iteration schemes for solving a class of nonlinear complementarity problems with the system matrix being an H-matrix. We establish the convergence theorems for the schemes. The numerical experiments show that the schemes are efficient for solving the class of nonlinear complementarity problems.