作者：
DAI YuHongKOU CaiXiaLSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems Science Chinese Academy of Sciences School of Science
Beijing University of Posts and Telecommunications
The linear conjugate gradient method is an optimal method for convex quadratic minimization due to the Krylov subspace minimization property. The proposition of limited-memory BFGS method and Barzilai-Borwein gradient...
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The linear conjugate gradient method is an optimal method for convex quadratic minimization due to the Krylov subspace minimization property. The proposition of limited-memory BFGS method and Barzilai-Borwein gradient method, however, heavily restricted the use of conjugate gradient method for largescale nonlinear optimization. This is, to the great extent, due to the requirement of a relatively exact line search at each iteration and the loss of conjugacy property of the search directions in various occasions. On the contrary, the limited-memory BFGS method and the Barzilai-Bowein gradient method share the so-called asymptotical one stepsize per line-search property, namely, the trial stepsize in the method will asymptotically be accepted by the line search when the iteration is close to the solution. This paper will focus on the analysis of the subspace minimization conjugate gradient method by Yuan and Stoer(1995). Specifically, if choosing the parameter in the method by combining the Barzilai-Borwein idea, we will be able to provide some efficient Barzilai-Borwein conjugate gradient(BBCG) methods. The initial numerical experiments show that one of the variants, BBCG3, is specially efficient among many others without line searches. This variant of the BBCG method might enjoy the asymptotical one stepsize per line-search property and become a strong candidate for large-scale nonlinear optimization.
In this paper,we develop the truncated Euler-Maruyama(EM)method for stochastic differential equations with piecewise continuous arguments(SDEPCAs),and consider the strong convergence theory under the local Lipschitz c...
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In this paper,we develop the truncated Euler-Maruyama(EM)method for stochastic differential equations with piecewise continuous arguments(SDEPCAs),and consider the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type *** order of convergence is ***,we show that the truncated EM method can preserve the exponential mean square stability of *** examples are provided to support our conclusions.
作者：
Lin, LeiLv, JunliangSchool of Mathematics
Jilin University Qianjin Street Jilin Province Changchun130012 China LSEC
Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China
Consider a time-harmonic acoustic plane wave incident onto an elastic body with an unbounded periodic surface. The medium above the surface is supposed to be filled with a homogeneous compressible inviscid air/fluid o...
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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. 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.
Inspired by the success of the projected Barzilai-Borwein (PBB) method for largescale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by exp...
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Inspired by the success of the projected Barzilai-Borwein (PBB) method for largescale box-constrained quadratic programming, we propose and analyze the monotone projected gradient methods in this paper. We show by experiments and analyses that for the new methods,it is generally a bad option to compute steplengths based on the negative gradients. Thus in our algorithms, some continuous or discontinuous projected gradients are used instead to compute the steplengths. Numerical experiments on a wide variety of test problems are presented, indicating that the new methods usually outperform the PBB method.
作者：
Wei-nan EPing-bing MingDepartment of Mathematics and PACM
Princeton University LSEC
Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China
We study continuum and atomistic models for the elastodynamics of crystalline solids at zero temperature. We establish sharp criterion for the regime of validity of the nonlinear elastic wave equations derived from th...
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We study continuum and atomistic models for the elastodynamics of crystalline solids at zero temperature. We establish sharp criterion for the regime of validity of the nonlinear elastic wave equations derived from the well-known Cauchy-Born rule.
Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement...
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Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. This algorithm is used in PHG, Parallel Hierarchical Grid Chttp：//lsec. cc. ac. cn/phg/）, a toolbox under active development for parallel adaptive finite element solutions of partial differential equations. The algorithm proposed is characterized by allowing simukaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given, which is useful in better understanding the behaviour of the biseetioning refinement procedure.
In this paper, we propose the component-consistent pressure correction projection method for the numerical solution of the incompressible Navier-Stokes equations. This projection preserves a discrete form of the compo...
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In this paper, we propose the component-consistent pressure correction projection method for the numerical solution of the incompressible Navier-Stokes equations. This projection preserves a discrete form of the component-consistent condition between components of the solution at every time step. We also propose, in particular, the CNMT2 + CCPC method and the RKMT + CCPC method, both involving one pressure Poisson solution per time step. We show that they are both of O(Delta t(2)) for the Velocity and O(Delta t) for the pressure on fixed meshes and finite time intervals. Numerical tests on flow simulation support our claim that the component-consistent pressure correction projection method solves the deviation problem encountered sometimes by the original pressure correction projection method.
A matrix splitting method is presented for minimizing a quadratic programming (QP) problem, and a general algorithm is designed to solve the QP problem and generates a sequence of iterative points. We prove that the s...
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A matrix splitting method is presented for minimizing a quadratic programming (QP) problem, and a general algorithm is designed to solve the QP problem and generates a sequence of iterative points. We prove that the sequence generated by the algorithm converges to the optimal solution and has an R-linear rate of convergence if the QP problem is strictly convex and nondegenerate, and that every accumulation point of the sequence generated by the general algorithm is a KKT point of the original problem under the hypothesis that the value of the objective function is bounded below on the constrained region, and that the sequence converges to a KKT point if the problem is nondegenerate and the constrained region is bounded.
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