Many stochastic models in queueing, inventory, communications, and dam theories, etc., result in the problem of numerically determining the minimal nonnegative solutions for a class of nonlinear matrix equations. Vari...
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Many stochastic models in queueing, inventory, communications, and dam theories, etc., result in the problem of numerically determining the minimal nonnegative solutions for a class of nonlinear matrix equations. Various iterative methods have been proposed to determine the matrices of interest. We propose a new, efficient successive-substitution Moser method and a Newton-Moser method which use the Moser formula (which, originally, is just the Schulz method). These new methods avoid the inverses of the matrices, and thus considerable savings on the computational workloads may be achieved. Moreover, they are much more suitable for implementing on parallel multiprocessor systems. Under certain conditions, we establish monotone convergence of these new methods, and prove local linear convergence for the substitution Moser method and superlinear convergence for the Newton-Moser method. (C) 1997 Elsevier Science Inc.
For the large-scale system of linear equations with symmetric positive definite block coefficient matrix resulting from the discretization of a self-adjoint elliptic boundary-value problem, by making use of the blocke...
For the large-scale system of linear equations with symmetric positive definite block coefficient matrix resulting from the discretization of a self-adjoint elliptic boundary-value problem, by making use of the blocked multilevel iteration idea, we construct preconditioning matrices for the coefficient matrix and set up a class of parallel hybrid algebraic multilevel iterative methods for solving this kind of system of linear equations. Theoretical analysis shows that not only do these new methods lend themselves to parallel computation, but also their convergence rates are independent of both the sizes and the level numbers of the grids, and their computational work loads are also hounded by linear functions of the step sizes of the finest grids. (C) 1997 Elsevier Science Inc.
A class of parallel hybrid iteration method and its accelerated overrelaxation variant are established for solving the large sparse block bordered system of linear equations, and their convergence are proved when the ...
A class of parallel hybrid iteration method and its accelerated overrelaxation variant are established for solving the large sparse block bordered system of linear equations, and their convergence are proved when the coefficient matrix of the linear system is an M-matrix, an II-matrix, and a symmetric positive definite matrix, respectively. (C) Elsevier Science Inc., 1997.
We set up a class of multi-parameter relaxed parallel matrix multisplitting methods for solving the linear complementarity problems on the SIMD multiprocessor systems. This class of methods can not only includes all t...
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We set up a class of multi-parameter relaxed parallel matrix multisplitting methods for solving the linear complementarity problems on the SIMD multiprocessor systems. This class of methods can not only includes all the existing relaxed methods for the linear complementarity problems, but also can yields a lot of novel ones in the sense of multisplitting. Thus, it is reasonably general. We set up the convergence theory of these relaxed methods under the condition that the system matrix is an H-matrix with positive diagonal elements.
In our previous paper[1] two weighted NND dtherence schemes were presentedby using proper weighted functions instead of minmod functions. As a result,the WNNDschemes enhance accuracy and yield smoother numrical auxes....
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In our previous paper[1] two weighted NND dtherence schemes were presentedby using proper weighted functions instead of minmod functions. As a result,the WNNDschemes enhance accuracy and yield smoother numrical auxes. In this paper two weightedENN schemes based on the ENN scheme[2] are constructed. The ENN scheme and WENNschemes are uniformly second-order accuracy and can achieve third-order accuracy in certainsmooth regions
This paper investigates the global convergence properties of the Fletcher-Reeves (FR) method for unconstrained optimization. In a simple way, we prove that a kind of inexact line search condition can ensure the conver...
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This paper investigates the global convergence properties of the Fletcher-Reeves (FR) method for unconstrained optimization. In a simple way, we prove that a kind of inexact line search condition can ensure the convergence of the FR method. Several examples are constructed to show that, if the search conditions are relaxed, the FR method may produce an ascent search direction, which implies that our result cannot be improved.
A class of hybrid algebraic multilevel preconditioning methods is presented for solving systems of linear equations with symmetric positive-definite matrices resulting from the discretization of many second-order elli...
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A class of hybrid algebraic multilevel preconditioning methods is presented for solving systems of linear equations with symmetric positive-definite matrices resulting from the discretization of many second-order elliptic boundary value problems by the finite element method. The new preconditioners are shown to be of optimal orders of complexities for 2-D and 3-D problem domains, and their relative condition numbers are estimated to be bounded uniformly with respect to the numbers of both levels and nodes.
We set up a class of parallel nonlinear multisplitting AOR methods by directly multisplitting the nonlinear mapping involved in the nonlinear complementarity problems. The different choices of the relaxation parameter...
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We set up a class of parallel nonlinear multisplitting AOR methods by directly multisplitting the nonlinear mapping involved in the nonlinear complementarity problems. The different choices of the relaxation parameters can yield all the known and a lot of new relaxation methods, as well as a lot of new relaxed parallel nonlinear multisplitting methods for solving the nonlinear complementarity problems. The two-sided approximation properties and the influences on the convergence rates from the relaxation parameters about our new methods are shown, and sufficient conditions guaranteeing the methods to converge globally are discussed. Finally, a lot of numerical results show that our new methods are feasible and efficient.
A new comparison theorem on the monotone convergence rates of the parallel nonlinear multisplitting accelerated overrelaxation (AOR) method for solving the large scale nonlinear complementarity problem is established....
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A new comparison theorem on the monotone convergence rates of the parallel nonlinear multisplitting accelerated overrelaxation (AOR) method for solving the large scale nonlinear complementarity problem is established. Thus, the monotone convergence theory of this class of method is completed.
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