谱约束下反自反矩阵的最佳逼近问题

该文研究了反自反矩阵的逆特征值问题及其最佳逼近问题,建立了反自反矩阵的逆特征值问题有解的充要条件,得到了解的表达式.进一步,对于任意给定的n阶复矩阵,得到了相关最佳逼近问题解的表达式.     

含空隙的各向同性介质Helmholtz方程扰动问题的传输特征值

传输特征值在反散射唯一性理论中具有十分重要的意义.在含空隙的各向同性非均匀介质折射率扰动下,研究了Helmholtz方程传输特征值的存在性问题.首先,通过构造Neumann-Dirichlet算子,建立传输特征值问题的等价形式.然后,进一步构造特征值函数,将扰动的传输特征值问题转化为算子为零特征值的扰动问题.最后,利用隐函数定理的扰动方法证明传输特征值的存在性.     

求解陀螺系统特征值问题的收缩二阶Lanczos方法

本文研究陀螺系统特征值问题的数值解法,利用反对称矩阵Lanczos算法,提出了求解陀螺系统特征值问题的二阶Lanczos方法.基于提出的陀螺系统特征值问题的非等价低秩收缩技术,给出了计算陀螺系统极端特征值的收缩二阶Lanczos方法.数值结果说明了算法的有效性.     

一类特殊矩阵的特征值反问题

§1 引言 关于特征值反问题的历史沿革,作者在文[1]中已经作了介绍,当前研究得比较成熟的是对称三对角矩阵的特征值反问题。作者在文[2]中提供了一个对称三对角矩阵特征值反问题的实际应用例子。本文考虑如下形状矩阵的特征值反问题:设     

一类二阶微分方程的特征值估计及其反问题

借助Rouché定理及渐近分析的方法,给出了边界条件含有特征参数的一类二阶微分方程的特征值渐近公式.运用特征值渐近公式给出了特征值反问题的一个惟一性结果及重构公式.     

一类Sturm-Liouville问题特征的渐近分析

考虑[0,1]上带第三类边界条件的S-L问题特征值的渐近表示.利用已有的渐近性结果及Fr啨chet导数技术,对特征值进行了精细的分析,清楚地给出了边界条件中的常数(h,H)对特征值的影响.本文的工作对S-L问题的一类反谱问题及相关微分方程反问题的唯一性结果有着重要的应用,也为专著[4,6]中的某些关键结果提供了一个简化的证明途径.     

一类基于Robin边界条件变化的反传输特征值问题

本文研究具有Robin边界条件的Schr?dinger算子反传输特征值问题,旨在由传输特征值数据还原势函数.通过改变其中一个边界条件参数,可以获得有无穷多个能量有限的传输特征值.本文证明这样的传输特征值集合可以唯一地确定Schr?dinger算子的势函数及另一个边界条件参数.     

求解特征值反问题的一种迭代法

关于特征值反问题的算法,已讨论许多,见[1]—[5].到目前为止,主要的算法是用Newton法解相应的非线性方程组.然而,代数特征值反问题是一类矩阵计算问题,因此,有可能利用矩阵的性质构造简单的算法,而不仅仅是把它作为一个通常的非线性问题加以处理.基于这种思想.本文给出一个利用矩阵性质的线性收敛迭代法.     

对称正交反对称矩阵反问题解存在的条件

矩阵反问题和矩阵特征值反问题在科学和工程技术中具有广泛的应用,有关它们的研究已取得了许多进展[1,2].[3]和[4]分别研究了反对称矩阵反问题和双反对称矩阵特征值反问题等.本文研究一类更广泛的对称正交反对称矩阵反问题.用Rn×m（Cn×m）表示n×m实（复）矩阵的全体,ASRn×n表示n阶反对称矩阵的全体,ABSRn×n表示n阶双反对称矩阵的全体,ORn×n表示n阶正交矩阵的全体.A+表示矩阵A的Moore-Penrose广义逆.In表示n阶单位矩阵.ei表示n阶单位矩阵的第i列,Sn=[en,en-1,     

次正规矩阵、次酉矩阵、次厄米特矩阵及反次厄米特矩阵

主要研究了下列几方面问题:(i)次酉矩阵、次厄米特矩阵及反次厄米特矩阵的特征值与次特征值;(ii)次正规矩阵、次酉矩阵、次厄米特矩阵及反次厄米特矩阵分别与正规矩阵、酉矩阵、厄米特矩阵及反厄米特矩阵之间的关系;(iii)次正规矩阵、次酉矩阵、次厄米特矩阵及反次厄米特矩阵之间的联系.     

A Newton iteration process for inverse eigenvalue problems

Summary We suppose an inverse eigenvalue problem which includes the classical additive and multiplicative inverse eigenvalue problems as special cases. For the numerical solution of this problem we propose a Newton iteration process and compare it with a known method. Finally we apply it to a numerical example.     

Inverse unitary eigenproblems and related orthogonal functions

Summary. This paper explores the relationship between certain inverse unitary eigenvalue problems and orthogonal functions. In particular, the inverse eigenvalue problems for unitary Hessenberg matrices and for Schur parameter pencils are considered. The Szeg? recursion is known to be identical to the Arnoldi process and can be seen as an algorithm for solving an inverse unitary Hessenberg eigenvalue problem. Reformulation of this inverse unitary Hessenberg eigenvalue problem yields an inverse eigenvalue problem for Schur parameter pencils. It is shown that solving this inverse eigenvalue problem is equivalent to computing Laurent polynomials orthogonal on the unit circle. Efficient and reliable algorithms for solving the inverse unitary eigenvalue problems are given which require only O() arithmetic operations as compared with O() operations needed for algorithms that ignore the structure of the problem. Received April 3, 1995 / Revised version received August 29, 1996     

Computational methods of linear algebra

The authors' survey paper is devoted to the present state of computational methods in linear algebra. Questions discussed are the means and methods of estimating the quality of numerical solution of computational problems, the generalized inverse of a matrix, the solution of systems with rectangular and poorly conditioned matrices, the inverse eigenvalue problem, and more traditional questions such as algebraic eigenvalue problems and the solution of systems with a square matrix (by direct and iterative methods).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 54, pp. 3–228, 1975.     

A NOTE ON THE BACKWARD ERRORS FOR INVERSE EIGENVALUE PROBLEMS

In this note,we consider the backward errors for more general inverse eigenvalus prob-lems by extending Sun‘‘‘‘s approach.The optimal backward errors defined for diagonal-ization matrix inverse eigenvalue problem with respect to an approximate solution,and the upper and lower bounds are derived for the optimal backward errors.The results may be useful for testing the stability of practical algorithms.     

INVERSE EIGENVALUE PROBLEM OF HERMITIAN GENERALIZED ANTI-HAMILTONIAN MATRICES

§1　IntroductionWe considerthe following inverse eigenvalue problem offinding an n-by-n matrix A∈S such thatAxi =λixi,i =1,2 ,...,m,where S is a given set of n-by-n matrices,x1 ,...,xm(m≤n) are given n-vectors andλ1 ,...,λmare given constants.Let X=(x1 ,...,xm) ,Λ=(λ1 ,λ2 ,...,λm) ,then the above inverse eigenvalue problemcan be written as followsProblem Given X∈Cn×m,Λ=(λ1 ,...,λm) ,find A∈S such thatAX =XΛ,where S is a given matrix set.We also discuss the so-called opti…     

HGAH矩阵的逆特征值问题

In this paper, the inverse eigenvalue problem of Hermitian generalized anti-Hamihonian matrices and relevant optimal approximate problem are considered. The necessary and sufficient conditions of the solvability for inverse eigenvalue problem and an expression of the general solution of the problem are derived. The solution of the relevant optimal approximate problem is given.     

The constrained inverse eigenvalue problem and its approximation for normal matrices

In this paper, the constrained inverse eigenvalue problem and associated approximation problem for normal matrices are considered. The solvability conditions and general solutions of the constrained inverse eigenvalue problem are presented, and the expression of the solution for the optimal approximation problem is obtained.     

An Approach to Solving Inverse Eigenvalue Problems for Matrices

The paper considers different formulations of inverse eigenvalue problems for matrices whose entries either polynomially or rationally depend on unknown parameters. An approach to solving inverse problems together with numerical algorithms is suggested. The solution of inverse problems is reduced to the problem of finding the so-called discrete solutions of nonlinear algebraic systems. The corresponding systems are constructed using the method of traces, and their discrete roots are found by applying the algorithms for solving nonlinear algebraic systems in several variables previously suggested by the author. Bibliography: 30 titles.     

k次R-对称矩阵的特征值反问题及最佳逼近问题

<正>1引言在[7]中,Trench推广了中心对称矩阵和自反矩阵的概念定义了R-对称矩阵,采用一个统一的方式证明了许多已有的结论并得到更强的结果.在Trench工作的基础上,文[6]定义了k次R-对称矩阵,并指出对于任意奇异的Hermitian矩阵A,都存在k次单位矩阵R     

The solvability conditions for the inverse eigenvalue problems of reflexive matrices

This paper involves related inverse eigenvalue problems of reflexive matrices and their optimal approximation, the sufficient and necessary conditions under which the solvable problems of inverse eigenvalue, and the general provided form of the solution. Furthermore, the algorithm to compute the optimal approximate solution and some numerical experiments are given.