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Estimations on upper and lower bounds of solutions to a class of tensor complementarity problems

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Frontiers of Mathematics in China 2019年第3期14卷 661-671页

作者： Yang XU Weizhe GU Zheng-Hai HUANG School of Mathematics Tianjin University Tianjin 300350 China

We introduce a class of structured tensors, called generalized row strictly diagonally dominant tensors, and discuss some relationships between it and several classes of structured tensors, including nonnegative tensors, Btensors, and strictly copositive tensors. In particular, we give estimations on upper and lower bounds of solutions to the tensor complementarity problem (TCP) when the involved tensor is a generalized row strictly diagonally dominant tensor with all positive diagonal entries. The main advantage of the results obtained in this paper is that both bounds we obtained depend only on the tensor and constant vector involved in the TCP;and hence, they are very easy to calculate.

关键词： Tensor complementarity problem (TCP) generalized row strictly diagonally dominant tensor upper and lower bounds of solutions

A parallel method for numerical solution of delay differential equations

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Journal of Harbin Institute of Technology(New Series) 2000年第3期7卷 37-39页

作者：丁效华刘明珠 Dept. of Mathematics Harbin Institute of Technology Harbin 150001 China

A parallel diagonally iterated Runge Kutta (PDIRK) method is constructed to solve stiff initial value problems for delay differential equations. The order and stability of this PDIRK method has been analyzed, and the iteration parameters of the method are tuned in such a way that fast convergence to the value of corrector is achieved.

关键词： diagonally implicit RK methods parallel method corrector

Extrapolation of Explicit DIMSIMs of High Order to Solve the Ordinary Differential Equations

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Journal of Applied Mathematics and Physics 2019年第12期7卷 3022-3030页

作者： Ali J. Kadhim Annie Gorgey Mathematics Department Faculty of Science and Mathematics Universiti Pendidikan Sultan Idris Tanjong Malim Perak Malaysia

The purpose of this research is to investigate the effciency of explicit diagonally implicit multi-stage integration methods with extrapolation. The author gave detailed explanation of explicit diagonally implicit multi-stage integration method and compared the base method with a technique known as extrapolation to improve the effciency. Extrapolation for symmetric Runge-Kutta method is proven to improve the accuracy since with extrapolation the solutions exhibit asymptotic error expansion, however for General linear methods, it is not known whether extrapolation can improve the effciency or not. Therefore this research focuses on the numerical experimental results of the explicit diagonally implicit multistage integration with and without extrapolation for solving some ordinary differential equations. The numerical results showed that the base method with extrapolation is more effcient than the method without extrapolation.

关键词： Extrapolation Technique General Linear Methods diagonally Implicit Muti-Stage Integration Explicit Methods

On Classes of Matrices with Variants of the Diagonal Dominance Property

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Advances in Linear Algebra & Matrix Theory 2017年第2期7卷 37-65页

作者： Farid O. Farid Department of Mathematics Shanghai University Shanghai China

We study the relations between several classes of matrices with variants of the diagonal dominance property, and identify those classes which form pairs of incomparable classes. For an incomparable pair (X1,X2) of classes of matrices with variants of the diagonal dominance property, we also study the problem of providing sufficient conditions for the matrices in Xi to be in Xj with {i,j}={1,2}. The article is a continuation of a series of articles on the topic and related topics by the author;see [1][2][3][4].

关键词： Doubly diagonally Dominant Generalized diagonally Dominant (S1 S2) Separation Induced diagonally Dominant Row-Column diagonally Dominant with Index &alpha