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杜磊 副教授

2006年本科毕业于大连理工大学数学与应用数学专业,2008年硕士毕业于大连理工大学计算数学专业(导师:于波 教授),2011年博士毕业于日本名古屋大学计算理工学专攻,获博士(工学)学位(导师:张绍良 教授)。后在筑波大学计算机科学专攻从事博士后研究工作(日本技术振兴机构CREST项目资助,合作导师:Prof. SAKURAI Tetsuya)。2014年回国任职于大连理工大学数学科学学院。主要研究内容包括:大型稀疏线性方程组求解、矩阵特征值计算、高性能科学计算等。

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The GPBiCOR Method for Solving the General Matrix Equation and the General Discrete-Time Periodic Matrix Equations

发布时间: 2019-03-13 点击次数:

  • 论文类型:期刊论文
  • 第一作者:Selim, Basem, I
  • 通讯作者:Yu, B (reprint author), Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China.
  • 合写作者:Du, Lei,Yu, Bo
  • 发表刊物:IEEE ACCESS
  • 收录刊物:SCIE
  • 卷号:6
  • 页面范围:68649-68674
  • ISSN号:2169-3536
  • 关键字:GPBiCOR method; iterative method; general matrix equation; general periodic discrete-time matrix equations; Kronecker product; vectorization operator
  • 摘要:This paper is concerned with the numerical solutions of the general matrix equation Sigma(p)(i=1) Sigma(si)(j=1)A(ij)X(i)B(ij) = C, and the general discrete-time periodic matrix equations Sigma(p)(i=1) Sigma(si)(j=1)( A(i,j,k)X(i,k)B(i,j,k +) Ci,j,kXi,k+1Di,j,k) = M-k,M- for k = 1, 2, . . . , t, which include the well-known Lyapunov, Stein, and Sylvester matrix equations that appear in a wide range of applications in engineering and mechanical problems. Recently the generalized product-type BiCOR method, denoted as GPBiCOR, has been originally proposed to solve the nonsymmetric linear systems Ax = b, and its significant convergence performance has been confirmed in many numerical results. By applying the Kronecker product and the vectorization operator, we develop a matrix form of the GPBiCOR method to approximate the solutions of the above-mentioned general matrix equation and general discrete-time periodic matrix equations. We present the theoretical background of the extended GPBiCOR method and its main computational aspects. Furthermore, several numerical examples of matrix equations arising in different applications are considered to exhibit the accuracy and the efficiency of the proposed method as compared with other popular methods in the literature.
  • 发表时间:2018-01-01