检索结果-南通市图书馆

Chinese Quarterly Journal of Mathematics 2004年第3期19卷 286-291页

作者： LIUShu-qiang ZHANGHe-ruing DepartmentofBasicCourses TianjinUniversityofFinanceandEconomicsTianjin300222China GraduateSchool NankaiUniversityTianjin300071China

In this paper,we study real symmetric toeplitz matrices commutable with tridiagonal matrices, present more detailed results than those in [1], and extend them to nonsymmetric toeplitz matrices. Also, complex toeplitz ... 详细信息

关键词： matrix toeplitz matrix Hermite matrix

MODIFIED NEWTON＇S ALGORITHM FOR COMPUTING THE GROUP INVERSES OF SINGULAR toeplitz MATRICES

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 Computational Mathematics 2006年第5期24卷 647-656页

作者： Jian-feng Cai Michael K. Ng Yi-min Wei Department of Mathematics The Chinese University of Hong Kong Hong Kong Department of Mathematics Hong Kong Baptist University Hong Kong School of Mathematical Sciences Fudan University Shanghai 200433 China ~ Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University) Ministry of Education

Newton＇s iteration is modified for the computation of the group inverses of singular toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement rank. Because of the displacement structure of the iteration matrix, the matrix-vector multiplication involved in Newton＇s iteration can be done efficiently. We show that the convergence of the modified Newton iteration is still very fast. Numerical results are presented to demonstrate the fast convergence of the proposed method.

关键词： Newton's iteration Group inverse toeplitz matrix Displacement rank.

BANDED toeplitz PRECONDITIONERS FOR toeplitz MATRICES FROM SINC METHODS

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 Computational Mathematics 2012年第5期30卷 533-543页

作者： Zhi-Ru Ren LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

We give general expressions, analyze algebraic properties and derive eigenvalue bounds for a sequence of toeplitz matrices associated with the sinc discretizations of various orders of differential operators. We demonstrate that these toeplitz matrices can be satisfactorily preconditioned by certain banded toeplitz matrices through showing that the spectra of the preconditioned matrices are uniformly bounded. In particular, we also derive eigen- value bounds for the banded toeplitz preconditioners. These results are elementary in constructing high-quality structured preconditioners for the systems of linear equations arising from the sinc discretizations of ordinary and partial differential equations, and are useful in analyzing algebraic properties and deriving eigenvalue bounds for the correspond- ing preconditioned matrices. Numerical examples are given to show effectiveness of the banded toeplitz preconditioners.

关键词： toeplitz matrix Banded toeplitz preconditioner Generating function Sincmethod Eigenvalue bounds.

BANDED M-matrix SPLITTING PRECONDITIONER FOR RIESZ SPACE FRACTIONAL REACTION-DISPERSION EQUATION

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 Computational Mathematics 2024年第2期42卷 372-389页

作者： Shiping Tang Aili Yang Yujiang Wu School of Mathematics and Statistics Lanzhou UniversityLanzhou 730000China School of Mathematics and Statistics Hainan Normal UniversityHaikou 570000China

Based on the Crank-Nicolson and the weighted and shifted Grunwald operators,we present an implicit difference scheme for the Riesz space fractional reaction-dispersion equations and also analyze the stability and the convergence of this implicit difference ***,after estimating the condition number of the coefficient matrix of the discretized scheme,we find that this coefficient matrix is ill-conditioned when the spatial mesh-size is sufficiently *** overcome this deficiency,we further develop an effective banded M-matrix splitting preconditioner for the coefficient *** properties of this preconditioner together with its preconditioning effect are ***,Numerical examples are employed to test the robustness and the effectiveness of the proposed preconditioner.

关键词： Riesz space fractional equations toeplitz matrix conjugate gradient method Incomplete Cholesky decomposition Banded M-matrix splitting

ON STRUCTURED VARIANTS OF MODIFIED HSS ITERATION METHODS FOR COMPLEX toeplitz LINEAR SYSTEMS

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 Computational Mathematics 2013年第1期31卷 57-67页

作者： Fang Chen Yaolin Jiang Qingquan Liu Department of Mathematical Sciences Xi'an Jiaotong University Xi'an 710049 China Key Laboratory of Environmental Mechanics Institute of Mechanics Chinese Academy of Sciences Beijing 100190 China

The Modified Hermitian and skew-Hermitian splitting （MHSS） iteration method was presented and studied by Bai, Benzi and Chen （Computing, 87（2010）, 93-111） for solving a class of complex symmetric linear systems. In this paper, using the properties of toeplitz matrix, we propose a class of structured MHSS iteration methods for solving the complex toeplitz linear system. Theoretical analysis shows that the structured MHSS iteration method is unconditionally convergent to the exact solution. When the MHSS iteration method is used directly to complex symmetric toeplitz linear systems, the computational costs can be considerately reduced by use of toeplitz structure. Finally, numerical ex- periments show that the structured MHSS iteration method and the structured MHSS preconditioner are efficient for solving the complex toeplitz linear system.

关键词： toeplitz matrix MHSS iteration method Complex symmetric linear system.

Novel algorithm on DOA estimation for correlated sources under complex symmetric toeplitz noise

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 Systems Engineering and Electronics 2008年第5期19卷 902-906页

作者： Wang Kai Zhang Yongshun Shi Dan Missile Inst. Air Force Engineering Univ. Sanyuan 713800 P. R. China Dept. of 61046 Beijing 100071 P. R. China

To cope with the scenario where both uncorrelated sources and coherent sources coexist, a novel algorithm to direction of arrival （DOA） estimation for symmetric uniform linear array is presented. Under the condition of stationary colored noise field, the algorithm employs a spatial differencing method to eliminate the noise covariance matrix and uncorrelated sources, then a toeplitz matrix is constructed for the remained coherent sources. After preprocessing, a propagator method （PM） is employed to find the DOAs without any eigendecomposition. The number of sources resolved by this approach can exceed the number of array elements at a lower computational complexity. Simulation results demonstrate the effectiveness and efficiency of the proposed method.

关键词： DOA estimation coherent source differencing toeplitz matrix propagator method.

Fast forward modeling of gravity anomalies for two-dimensional bodies of arbitrary shape and density distribution

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

Applied Geophysics 2020年第5期17卷 776-783,902,903页

作者： Chen Xin Chen Long-Wei Luo Tian-Ya Xiong Bin Guangxi Key Laboratory of Exploration for Hidden Metallic Ore Deposits College of Earth SciencesGuilin University of TechnologyGuilin 541006China Hubei Subsurface Multi-scale Imaging Key Laboratory Institute of Geophysics and GeomaticsChina University of GeosciencesWuhan 430074China

A fast and high precision spatial domain algorithm is presented for forward modeling of two-dimensional(2D)body gravity anomalies of arbitrary shape and density *** new algorithm takes advantage of the convolution properties of the expression for 2D gravity anomalies,uses a rectangular cell as a grid subdivision unit,and then 2D bodies with irregular cross-sections are approximated by a combination of 2D bodies with a rectangular cross *** closed-form expression is used to calculate the gravitational anomalies of the combination of 2D bodies with a rectangular cross *** improve computing effi ciency,the new algorithm uses a fast algorithm for the implementation of the toeplitz matrix and vector *** synthetic 2D models with rectangular and circular cross-sections and constant and variable densities are designed to evaluate the computational accuracy and speed of the new *** experiment results show that the computation costs less than 6 s for a grid subdivision with 10000×10000 *** to the traditional forward modeling methods,the proposed method significantly improved computational effi ciency while guaranteeing computational accuracy.

关键词： two-dimensional bodies gravity anomalies forward modeling toeplitz matrix

A New Computational Approach for Solving Optimal Control of Linear PDEs Problem

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2014年第3期30卷 735-748页

作者： M.Mahmoudi A.V.Kamyad S.Effati Department of Mathematics University of Qom Department of Mathematics Ferdowsi University of Mashhad

In this paper, we present a new computational approach for solving an internal optimal control problem, which is governed by a linear parabolic partial differential equation. Our approach is to approximate the PDE problem by a nonhomogeneous ordinary differential equation system in higher dimension. Then, the homogeneous part of ODES is solved using semigroup theory. In the next step, the convergence of this approach is verified by means of toeplitz matrix. In the rest of the paper, the optimal control problem is solved by utilizing the solution of homogeneous part. Finally, a numerical example is given.

关键词： optimal control parabolic partial differential equation semigroups theory, nonlinear programming toeplitz matrix

Commuting Solutions of a Quadratic matrix Equation for Nilpotent Matrices

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

Algebra Colloquium 2018年第1期25卷 31-44页

作者： Qixiang Dong Jiu Ding Qianglian Huang School of Mathematical Sciences Yangzhou University Yangzhou Jiangsu 225002 China Department of Mathematics University of Southern Mississippi Hattiesburg MS 39406 USA

We solve the quadratic matrix equation AXA = XAX with a given nilpotent matrix A, to find all commuting solutions. We first provide a key lemma, and consider the special case that A has only one Jordan block to motivate the idea for the general case. Our main result gives the structure of all the commuting solutions of the equation with an arbitrary nilpotent matrix.

关键词： quadratic matrix equation nilpotent matrix Jordan canonical form toeplitz matrix commuting solution