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ON THE LEAST SQUARES PROBLEM OF A MATRIXEQUATION

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Journal of Computational mathematics 1999年第6期17卷 589-594页

作者： An-ping Liao(college of Science, hunan normal university, changsha 410081, china) hunan normal Univ Coll Sci Changsha 410081 Peoples R China

Least squares solution of F=PG with respect to positive semidefinite symmetric P is considered,a new necessary and sufficient condition for solvablity is given,and the expression of solution is derived in the some special cases. Based on the expression, the least spuares solution of an inverse eigenvalue problem for positive semidefinite symmetric matrices is also given.

关键词： least squares solution matrix equation inverse eigenvalue problem positive semidefinite symmetric matrix

AN EXTREMAL APPROACH TO BIRKHOFF QUADRATURE FORMULAS

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Journal of Computational mathematics 2001年第5期19卷 459-466页

作者： Ying-guang Shi (Department of mathematics, hunan normal university, changsha 410081, china) 湖南师范大学湖南长沙 410081

Discusses an extremal problem with Birkhoff interpolation constraints. Quadrature formula derived from an extremal problem; Overview of auxiliary lemmas; Derivation of some properties of polynomials.

关键词： an extremal approach Birkhoff quadrature formulas

Determination of jumps for functions via derivative Gabor series

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Applied mathematics(A Journal of Chinese Universities) 2009年第2期24卷 191-199页

作者： ZHOU Ying-ying SHI Xian-liang college of mathematics and computer Science, hunan normal university,changsha 410081,china college of mathematics and computer Science Hunan Normal University Changsha 410081 China

Recently, Shi Xianliang and Hu Lan published the method of concentration factors for determination of jumps of functions via MCM conjugate wavelets. Usually, it is difficult to calculate the Hilbert transform of general window functions. The aim of this paper is to discuss determination of jumps for functions based on derivative Gabor series. The results will simplify the calculation of jump values.

关键词： jumps Gabor series derivative

SUPERCONVERGENCE ANALYSIS FOR CUBIC TRIANGULARELEMENT OF THE FINITE ELEMENTSUPERCONVERGENCE ANALYSIS FOR CUBIC TRIANGULARELEMENT OF THE FINITE ELEMENT

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Journal of Computational mathematics 2000年第5期18卷 541-550页

作者： Qi-ding Zhu (Department of mathematics, hunan normal university, changsha 410081, china ) 湖南师范大学湖南长沙 410081

In this paper, we construct a projection interpolation for cubic triangular element by using othogonal expansion triangular method. We show two fundamental formulas of estimation on a special partion and obtain a superconvergence result of 1- ∈order higher for the placement function and its tangential derivative on the third order Lobatto points and Gauss points on each edge of triangular element.

关键词： Finite element Superconvergence Projection interpolation.

The Asymptotic Behavior for Numerical Solution of a Volterra Equation

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Acta Mathematicae Applicatae Sinica 2003年第1期19卷 47-58页

作者： Da XuDepartment of mathematics, hunan normal university, changsha 410081, china Department of mathematics Hunan Normal University Changsha 410081 China

Abstract Long-time asymptotic stability and convergence properties for the numerical solution of a Volterra equation of parabolic type are studied. The methods are based on the first-second order backward difference methods. The memory term is approximated by the convolution quadrature and the interpolant quadrature. Discretization of the spatial partial differential operators by the finite element method is also considered.

关键词： Keywords Volterra equation convolution quadrature interpolant quadrature finite element asymptotic behavior

Boundedness in Lebesgue spaces for commutators of multilinear singular integrals and RBMO functions with non-doubling measures

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Science china mathematics 2007年第3期50卷 361-376页

作者： Jing-shi XU Department of mathematics, hunan normal university, changsha 410081, china Department of mathematics Hunan Normal University Changsha 410081 China

The boundedness in Lebesgue spaces for commutators generated by multilinear singular integrals and RMBO(μ) functions of Tolsa with non-doubling measures is obtained, provided that ∥μ∥ = ∞ and multilinear singular... 详细信息

关键词： multilinear singular integral commutator maximal function non-doubling measure RMBO(μ) function Primary 42B20 Secondary 42B25

Superconvergence for L^2-projection in finite elements

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Chinese Science Bulletin 1998年第1期43卷 22-24页

作者： CHEN Chuanmiao Institute of Computing, hunan normal university, changsha 410081, china hunan normal university Institute of Computing Changsha China

Two classes of superconvergence points for L 2 projection u\-n in n degree finite elements on uniform grids are shown by element analysis method. Superconvergence points of u n are n+1 order Gauss point G n+1 for odd d≥1 (so the endpoint of each element is of superconvergent), and n+1 order pointset Z n+1 for even n ≥2 (which includes the endpoints and midpoint), respectively. Symmetry point is only an important part of them.

关键词： superconvergence finite elements L 2 projection.

Mean Convergence of Lagrange Type Interpolation on an Arbitrary System of Nodes

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Acta Mathematicae Applicatae Sinica 2002年第2期18卷 277-288页

作者： Ying-guang ShiDepartment of mathematics, hunan normal university, changsha 410081, china & Academy of mathematics and System sciences, Chinese Academy of sciences, Beijing 100080, china Department of mathematics Hunan Normal University Changsha 410081 China Academy of mathematics and System sciences Chinese Academy of Sciences Beijing 100080 China

Sufficient conditions of convergence and rate of convergence for Lagrange type interpolation in the weighted Lp norm on an arbitrary system of nodes are given.

关键词： Lagrange type interpolation convergence rate of convergence

CONVERGENCE OF (0,1,2,3) INTERPOLATION ON AN ARBITRARY SYSTEM OF NODES

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Journal of Computational mathematics 2001年第2期19卷 151-156页

作者： Ying-guang Shi (Institute of Computation, hunan normal university, changsha 410081, china) (Institute of Computational mathematics and Scientific/Engineering Computing, Academy of mathematics and Systems sciences, Chinese Academy of sciences, Beijing 100 湖南师范大学湖南长沙 410081

Provides information on a study which simplified and improved convergence of (0,1,2,3) interpolation on an arbitrary system of nodes. Definitions and notations; Results; Conjectures.

关键词： Hermite interpolation Hermite-Fejer interpolation convergence