检索结果-南通市图书馆

Comparative study on order-reduced methods for linear third-order ordinary differential equations

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Frontiers of Mathematics in China 2012年第6期7卷 1151-1168页

作者： Zhiru REN State Key Laboratory of Scientific/Engineering Computing Institute of ComputationalMathematics and Scientific/Engineering Computing Academy of Mathematics andSystems Science Chinese Academy of Sciences P. O. Box 2719 Beijing 100190 China

The linear third-order ordinary differential equation （ODE） can be transformed into a system of two second-order ODEs by introducing a variable replacement, which is different from the common order-reduced approach. We choose the functions p（z） and q（x） in the variable replacement to get different cases of the special order-reduced system for the linear third-order ODE. We analyze the numerical behavior and algebraic properties of the systems of linear equations resulting from the sine diseretizations of these special second-order ODE systems. Then the block-diagonal preconditioner is used to accelerate the convergence of the krylov subspace iteration methods for solving the discretized system of linear equation. Numerical results show that these order-reduced methods are effective for solving the linear third-order ODEs.

关键词： third-order ordinary differential equation order-reduced method sine discretization preeonditioner krylov subspace method

AINV AND BILUM PRECONDITIONING TECHNIQUES

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Applied Mathematics and Mechanics(English Edition) 2004年第9期25卷 1012-1021页

作者：谷同祥迟学斌刘兴平 Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Supercomputing Center of Computer Network Information Center Chinese Academy of Science

It was proposed that a robust and efficient parallelizable preconditioner for solving general sparse linear systems of equations, in which the use of sparse approximate inverse (AINV) techniques in a multi-level block ILU (BILUM) preconditioner were investigated. The resulting preconditioner retains robustness of BILUM preconditioner and has two advantages over the standard BILUM preconditioner: the ability to control sparsity and increased parallelism. Numerical experiments are used to show the effectiveness and efficiency of the new preconditioner.

关键词： sparse matrix preconditioning technique BILUM AINV krylov subspace method

Matrix-Free Physics-Based Preconditioned krylov subspace methods for 2D Particle Transport Problem

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

Matrix-Free Physics-Based Preconditioned Krylov Subspace Met...

第十六届全国流体力学数值方法研讨会2013

作者： Tong-Xiang Gu Yan-Hua Cao Mao-Sheng Li Xing-Ping Liu Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Department of Mathematics North China Electric Power University Research Center of Magnetic Driven Fusion Institute of Applied Physics and Computational Mathematics

＜正＞Source iteration is a iterative process usually used to solve the particle transport problem. For physical system containing subregions that are optically thick and scattering-dominated, most of the particles undergo many collisions before being captured or leaking out, source iteration is inefficient and costly. In this paper,

关键词： Particle transport Matrix-free Physics-based preconditioner krylov subspace method Source iteration

来源： cnki会议评论

在线全文

cnki会议

学校读者我要写书评

暂无评论

Communications in Mathematics and Statistics 2014年第2期2卷 139-153页

作者： Ren-Cang Li Qiang Ye Department of Mathematics University of Texas at ArlingtonP.O.Box 19408ArlingtonTX 76019-0408USA Department of Mathematics University of KentuckyLexingtonKY 40506USA

We present simultaneous reduction algorithms for two(nonsymmetric)matrices A and B to upper Hessenberg and lower Hessenberg forms,*** is through the simultaneous similarity reduction and the other is through a Lanczos–Arnoldi-type *** algorithm that uses the Lanczos–Arnoldi-type iteration can be considered as a generalization of both the nonsymmetric Lanczos algorithm and the standard Arnoldi *** shall also apply our reduction to construct a model reduction for certain kind second-order single-input single-output *** is proved that the model reduction has the desirable moment matching property.

关键词： Simultaneous reductions Lanczos–Arnoldi iteration krylov subspace method Model reduction

The GPBiCG(m, l) method for Solving General Matrix Equations

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Mathematical Research with Applications 2019年第4期39卷 408-432页

作者： Basem I.Selim Lei DU Bo YU Xuanru ZHU School of Mathematical Sciences Dalian University of Technology Mathematics and Computer Science Department Faculty of Science Menoufia University

The generalized product bi-conjugate gradient(GPBiCG(m,l))method has been recently proposed as a hybrid variant of the GPBi CG and the Bi CGSTAB methods to solve the linear system Ax=b with non-symmetric coefficient matrix,and its attractive convergence behavior has been authenticated in many numerical *** means of the Kronecker product and the vectorization operator,this paper aims to develop the GPBi CG(m,l)method to solve the general matrix equation■ and the general discrete-time periodic matrix equations■ which include the well-known Lyapunov,Stein,and Sylvester matrix equations that arise in a wide variety of applications in engineering,communications and scientific *** accuracy and efficiency of the extended GPBi CG(m,l)method assessed against some existing iterative methods are illustrated by several numerical experiments.

关键词： GPBiCG(m,l) method krylov subspace method matrix equations Kronecker product vectorization operator

A Two-Level Preconditioning Technique for Wire Antennas Attached with Dielectric Objects

同方期刊数据库评论

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Journal of Electronic Science and Technology 2011年第1期9卷 90-94页

作者： Zhi-Gang Ren Ting-Zhu Huang Liang Li the School of Mathematical Science University of Electronic Science and Technology of China Chengdu 610054 China

An iterative solution of linear systems is studied,which arises from the discretization of a wire antennas attached with dielectric objects by the hybrid finite-element method and the method of moment （hybrid FEM-MoM）.It is efficient to model such electromagnetic problems by hybrid FEM-MoM,since it takes both the advantages of FEM＇s and MoM＇s *** the resulted linear systems are complicated,and it is hard to be solved by krylov subspace methods alone,so a two-level preconditioning technique will be studied and applied to accelerate the convergence rate of the krylov subspace *** results show the effectiveness of the proposed two-level preconditioning technique.

关键词： Finite element method hybrid finite element method and method of moment krylov subspace method precondition.

Some Results on the Range-Restricted GMRES method

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

Journal of Applied Mathematics and Physics 2023年第12期11卷 3902-3908页

作者： Yiqin Lin School of Science Hunan University of Science and Engineering Yongzhou China

In this paper we reconsider the range-restricted GMRES (RRGMRES) method for solving nonsymmetric linear systems. We first review an important result for the usual GMRES method. Then we give an example to show that the range-restricted GMRES method does not admit such a result. Finally, we give a modified result for the range-restricted GMRES method. We point out that the modified version can be used to show that the range-restricted GMRES method is also a regularization method for solving linear ill-posed problems.

关键词： Nonsymmetric Linear System krylov subspace method Arnoldi Process GMRES RRGMRES