胡锡炎
应用数学与计算数学
个性化签名
- 姓名:胡锡炎
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学术头衔:
博士生导师
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学科领域:
应用数学
- 研究兴趣:应用数学与计算数学
胡锡炎,男,1939年生人,1963年毕业于武汉大学数学系计算数学专业,同年8月分配到湖南大学工作,1994年晋升为教授,1998年评定为博士生指导教师,曾任湖南省计算数学应用软件学会常务副理事长兼秘书长(1997-2000),副理事长(2001-2003),现任常务理事,长期从事数值代数的研究,1980年以来,开展约束矩阵方程的理论与算法研究,建立了学术梯队。
主要研究方向:应用数学与计算数学。培养了13名博士生(已有7名毕业,全部参与做博士后的研究工作),20余名硕士,已主持完成国家自然科学基金项目《矩阵特征对反问题及其高效算法》(1996-1998)和《约束矩阵方程及其数值解法》(1999-2001),目前主持国家自然科学基金项目《约束矩阵方程及其最佳逼近》的研究,已在《计算数学》、《系统科学与数学》、《应用数学学报》、《J. Comput. Math》、《SIAM J. Matrix Anal. Appl.》、《Appl. Math. Comput.》、《Inverse Problems》、《Numerical Linear Algebra Appl.》、《Linear Algebra Appl.》等国内外重要杂志和著名杂志上发表论文八十余篇,近三年有十余篇被SCI收录,1996年、1998年、2000年和2002年有五篇学术论文获得湖南省自然科学优秀论文奖,1996年获得机械工业部科技进步奖。
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560
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胡锡炎, 张磊, 周富照
计算数学,2003,25(1):13~22,-0001,():
-1年11月30日
Let P ∈ Rn×n such that pT=p, p-1=pT. A ∈ Rn×n is termed symmetric orthogonal symmetric matrix ifAT=A, (PA)T=PA.We denote the set of all n×n symmetric orthogonal symmetric matrices by SRn/p×nThis paper discuss the following two problems:Problem I. Given X Rnxm, A=diag(λ1,λ2...,λm). Find A ∈SRn/p×nsuch thatAX = XA.Problem Ⅱ. Given A ∈Rn×n. Find A* ∈SE such that‖A-A*‖=in/A∈SE‖A-A*‖where SE is the solution set of Problem I, ‖A-A*‖is the Frobenius norm In this paper, the sufficient and necessary conditions under which SE is nonemptyare obtained. The general form of SE has been given. The expression of the solu-tion A* of Problem II is presented. We have proved that some results of Reference[3] are the special cases of this paper.
对称正交对称矩阵,, 矩阵范数,, 最佳逼近
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胡锡炎, 张磊, 彭振赟
计算数学,2000,22(3):345~354,-0001,():
-1年11月30日
This paper considers the problem of constructing a Jacobi matrix from its defec-tive eigen-pair and a principal submatrix. Some necessary and sufficient conditionsof solvability have been derived. An algorithm and two numerical examples havebeen given.
Jacobi矩阵,, 主子阵,, 缺损特征对
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胡锡炎, 彭振赘, 张磊
计算数学,2005,27(1):11~18,-0001,():
-1年11月30日
给定矩阵X和B,得到了矩阵方程XTAX=B有双对称解的充分必要条件及有解时解的一般表达式。用SE表示此矩阵方程的解集合,证明了SE中存在唯一的矩阵A,使得A与给定矩阵A*的差的nbenius范数最小,并且给出了矩阵A的表达式。
双对称矩阵,, 矩阵方程,, 反问题,, 最佳逼近
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63浏览
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胡锡炎, 张磊, 黄贤通
系统科学与数学,1998,18(4):410~416,-0001,():
-1年11月30日
本文研究了两个Jacobi矩阵的逆特征问题:I给定实数λ,μ(λ>μ)和n维非零实向量x1,y1求n阶Jacobi矩阵J1使Jz=λx,Jy=μy,且λ>λ2(J)>…>λ2-1(J)>,λ>λ1+1(J)>…>λn(J),或λl(J)>λ2(J)>…λ1-1(J)>λ>λi+l(J)>…>λn-1(J)>μ。Ⅱ给定实数λ1μ(λ>μ)和n维非零实向量x1y1求n阶Jacobi矩阵J,使Jx=Az=λy=Jy,且λ1(J)>λ2(J)>…>λ2(J)>λ>λ>μ>λ1+2(J)>…>An(J)文中给出了问题Ⅰ,Ⅱ有唯一解的充要条件,并给出了解的表达式。
Jacobi矩阵,, 逆特征问题,, 特征值和特征向量
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胡锡炎, 周富照, 张磊
高等学校计算数学学报,2002,9(3):265~272,-0001,():
-1年11月30日
This paper discusses the optimal approximation to centro-symmetricmatrices on a linear manifold. The expression of the solution to these problems isgiven. Numerical methods of the optimal approximation to a matrix by matricesof a given class and numerical experiments are described.
linear manifold,, centro-symmetric matrix,, inverse problem of ma-trix,, optimal approximation.,
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胡锡炎, Xiao-ping Pan∗, Xi-yan Hu, Lei Zhang
Linear Algebra and its Applications 408 (2005) 66-77,-0001,():
-1年11月30日
In this paper, a class of constrained inverse eigenproblem and associated approximationproblem for skew symmetric and centrosymmetric matrices are essentially decomposed intothe same kind subproblems for real antisymmetric matrices with smaller dimensions.We presentthe general solution of the constrained inverse eigenproblem for skew symmetric andcentrosymmetric matrices in real number field. In addition, in corresponding solution set ofthe constrained inverse eigenproblem for skew symmetric and centrosymmetric matrices, theexplicit expression of the nearest matrix to a given matrix in the Frobenius norm is obtained.
Skew symmetric and centrosymmetric matrix, Constrained inverse eigenproblem, Approximation problem, Frobenius norm
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【期刊论文】The skew-symmetric orthogonal solutionsof the matrix equation AX=B☆
胡锡炎, Chunjun Meng∗, Xiyan Hu, Lei Zhang
Linear Algebra and its Applications 402 (2005) 303-318,-0001,():
-1年11月30日
An n×n real matrix X is said to be a skew-symmetric orthogonal matrix if XT=−Xand XTX =I. Using the special form of the C-S decomposition of an orthogonal matrixwith skew-symmetric k×k leading principal submatrix, this paper establishes the necessaryand sufficient conditions for the existence of and the expressions for the skew-symmetricorthogonal solutions of the matrix equation AX=B. In addition, in corresponding solutionset of the equation, the explicit expression of the nearest matrix to a given matrix in theFrobenius norm have been provided. Furthermore, the Procrustes problem of skew-symmetricorthogonal matrices is considered and the formula solutions are provided. Finally an algorithmis proposed for solving the first and third problems. Numerical experiments show that it isfeasible.
Skew-symmetric orthogonal matrix, Leading principal submatrix, C–S decomposition, The matrix nearness problem, The least-square solutions
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【期刊论文】The best approximation of matricesunder inequality constraints
胡锡炎, Xi-Yan Hu a, *, Lei Zhang b, Qin Zhang a
Applied Mathematics and Computation 137 (2003) 487-497,-0001,():
-1年11月30日
In this paper, a class of best approximation problems of matrices under inequalityconstraints are firstly presented and studied. For real matrices, symmetric matrices andantisymmetric matrices respectively, we have given the conditions for the existence ofsolutions and expressions of general solutions. Furthermore, the best approximationsolutions and algorithms of them are provided.
Best approximation, Inequality constraints, Inverse problem, Linear complementarity problem
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【期刊论文】The solvability conditions for the inverse eigenvalue problemof the symmetrizable matrices
胡锡炎, Yuanbei Deng, Xiyan Hu∗, Lei Zhang
Journal of Computational and Applied Mathematics 163 (2004) 101-106,-0001,():
-1年11月30日
The necessary and sufficient conditions for the solvability of the inverse eigenvalue problem AX=X over the class of the symmetrizable matrices are discussed, the general expression of the solution is given. Moreover, the related optimal approximation problem to a given matrix over the solution set is solved.
Symmetrizable matrices, Inverse eigenvalue problem, Optimal approximation, Matrix norm
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