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.
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.
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.
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.
The DFP method is one of the most famous numerical algorithms for unconstrained optimization. For uniformly convex objective functions convergence properties of the DFP method are studied. Several conditions that can ...
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The DFP method is one of the most famous numerical algorithms for unconstrained optimization. For uniformly convex objective functions convergence properties of the DFP method are studied. Several conditions that can ensure the global convergence of the DFP method are given.
This paper reveals the inner links between two known frameworks of multisplitting relaxation methods as completely as possible. By meticulously investigating the specific structures of these two frameworks, the asympt...
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A multigrid solver for the steady incompressible Navier-Stokes equations on a curvilinear grid is constructed. The Cartesian velocity components are used in the discretization of the momentum equations. A staggered, g...
A multigrid solver for the steady incompressible Navier-Stokes equations on a curvilinear grid is constructed. The Cartesian velocity components are used in the discretization of the momentum equations. A staggered, geometrically symmetric distribution of velocity components is adopted which eliminates spurious pressure oscillations and facilitates the transformation between Cartesian and co-or contravariant velocity components. The SCGS (symmetrical collective Gauss-Seidel) relaxation scheme proposed by Vanka on a Cartesian grid is extended to this case to serve as the smoothing procedure of the multigrid solver, in both ''box'' and ''box-line'' versions. Due to the symmetric distribution of velocity components of this scheme, the convergence rate and numerical accuracy are not affected by grid orientation, in contrast to a scheme proposed in the literature in which difficulties arise when the grid lines turn 90-degrees from the Cartesian coordinates. Some preliminary numerical experiences with this scheme are presented. (C) 1994 Academic Press. Inc.
In this paper, we construct Poisson difference schemes of any order accuracy based on Pade approximation for linear Hamiltonian systems on Poisson manifolds with constant coefficients. For nonlinear Hamiltonian system...
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In this paper, we construct Poisson difference schemes of any order accuracy based on Pade approximation for linear Hamiltonian systems on Poisson manifolds with constant coefficients. For nonlinear Hamiltonian systems on Poisson manifolds, we point out that symplectic diagonal implicit Runge-Kutta methods are also Poisson schemes. The preservation of distinguished functions and quadratic first integrals of the original Hamiltonian systems of these schemes are also discussed.
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