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1.
本文利用Thiele倒差分方法、Pade逼近方法、广义Q.D.算法及ε-算法等构造了几种广义有理样条函数.此外,通过直接法构造了(k-1,k)-型广义有理样条,给出了它的行列式表示和余项表示并证明了广义有理样条算子的存在性、唯一性、齐次性及连续性.  相似文献   

2.
顾传青 《计算数学》1997,19(1):19-28
1.引言矩阵Pade逼近在变分原理、在原子及初等粒子物理中已有深入的实际应用背景([1,2]).由于原有的矩阵Pade逼近都要涉及矩阵的乘法,而矩阵的乘法一般不满足交换律,从而在一定程度上限制了该逼近方法的应用范围.本文给出一种新的基于广义过的矩阵Pade逼近,它与原有的矩阵Pade逼近方法相比具有下列特点:第一.在构造过程中不需用到矩阵的乘法运算,没有左、右Pade逼近的区别,从而拓宽了应用范围(见下面说明),并且蕴含着它在数值分析和实际问题中的应用价值.第二,它可以用两种不同的格式计算出来:(1)分母多项式的显式…  相似文献   

3.
二元矩阵Pad6一型逼近的计算比较复杂.本文受Benouahmane和Cuyt的启发,通过引入一种变量代换,将二元齐次矩阵形式幂级数转化为一元含参数形式的矩阵形式幂级数,并给出了二元齐次矩阵Pad6一型逼近的构造性的定义和误差公式的证明.数值实例说明了此方法的有效性.  相似文献   

4.
该文讨论了线性流形上矩阵方程AX=B反对称正交对称反问题的最小二乘解及其最佳逼近问题.给出了最小二乘问题解集合的表达式,得到了给定矩阵的最佳逼近问题的解,最后给出计算任意矩阵的最佳逼近解的数值方法及算例.  相似文献   

5.
反对称正交对称矩阵反问题   总被引:6,自引:0,他引:6  
周富照  胡锡炎 《数学杂志》2005,25(2):179-184
本文讨论一类反对称正交对称矩阵反问题及其最佳逼近.研究了这类矩阵的一些性质,利用这些性质给出了反问题解存在的一些条件和解的一般表达式,不仅证明了最佳逼近解的存在唯一性,而且给出了此解的具体表达式.  相似文献   

6.
二元Thile型向量有理插值的误差公式   总被引:1,自引:0,他引:1  
借助于Somelson广义逆,文[1]首次讨论了多元向量有理插值问题.本文得到了二元Thiele型向量有理插值的一个精确的误差公式.  相似文献   

7.
利用矩阵的奇异值分解及广义逆,给出了矩阵约束下矩阵反问题AX=B有实对称解的充分必要条件及其通解的表达式.此外,给出了在矩阵方程的解集合中与给定矩阵的最佳逼近解的表达式.  相似文献   

8.
本文着重研究了定义在不规则结构上二元Thiele型有理插值问题,给出了相应的插值公式.  相似文献   

9.
徐仲  陆全 《工科数学》1999,15(1):81-83
Toeplitz矩阵Tn=(ti-j)n/i·j=0在信号处理、系统理论、逼近论、正交多项式.积分方程数值解等许多领域常常遇到,易知,Toeplitz矩阵T.的逆矩阵一般不再是Toeplitz矩阵.1972年Gohberg和Semencul给出了一个名结果:如果将Toeplirz矩阵T。  相似文献   

10.
研究正规矩阵束的Rayleigh商,证明了残差极小性质和特征值二阶逼近性质.所得结果独立于已有结果,而且本文方法和结果可用于研究更一般的正则矩阵束的Rayleigh商.  相似文献   

11.
一个二元矩阵插值连分式的展开式   总被引:2,自引:1,他引:1  
本文借助于文[1]定义的一种实用的矩阵广义逆,构造了一个二元Stieltjes型矩阵值插值连分式的展开式,它的截断分式可以定义二元矩阵值插值函数.  相似文献   

12.
首先提出了二元对角向量值有理插值问题,它包括主对角和副对角两种向量值有理插值,并分别给出了主对角线和副对角线上向量值有理插值的两种算法,即直接求系数bi,j的算法和基于Samelson广义逆所定义的特殊初等变换的矩阵算法.然后构造了在预给极点情况下求主对角线和副对角线上向量值有理插值的矩阵算法.最后给出多个数值例子说明上述算法的有效性.  相似文献   

13.
基于广义逆的多元矩阵有理插值   总被引:3,自引:1,他引:2  
本文借助于文[5]给出的一种矩阵广义逆,构造了二元Stieltjes型矩阵连分式的截断连分式,以此首次定义了平面上拟三角形网格上的二元矩阵有理插道值函数。文中给出了存在性的一个有用的判别条件。重要的特征定理和唯一性定理得到证明,并借助了实例说明了本文的结果。  相似文献   

14.
The main result of this paper is a generalization of the Mittag-Leffler theorem to matrix and operator valued meromorphic functions. Namely, a meromorphic matrix or operator valued function is constructed when the singular parts of the function and if its inverse are given in all singular points (which are assumed to be isolated). The paper contains also interpolation theorems based on other forms of local data (Jordan chains from left and right of the function and its inverse). An analysis of the local data, which is used in the proofs of these theorems is also included.Dedicated to the memory of D.P. MilmanThe research of this author partially supported by the Fund for Basic Research administrated by the Israel Academy of Science and Humanities.  相似文献   

15.
The inverse input impedance problem is investigated in the class of canonical integral systems with matrizants that are strongly regular J-inner matrix valued functions in the sense introduced in [ArD1]. The set of solutions for a problem with a given input impedance matrix (i.e., Weyl- Titchmarsh function) is parameterized by chains of associated pairs of entire inner p × p matrix valued functions. In our considerations the given data for the inverse bitangential input impedance problem is such a chain and an input impedance matrix, i.e., a p × p matrix valued function in the Carathéodory class. Existence and uniqueness theorems for the solution of this problem are obtained by consideration of a corresponding family of generalized bitangential Carathéodory interpolation problems. The connection between the inverse bitangential input scattering problem that was studied in [ArD4] and the bitangential input impedance problem is also exploited. The successive sections deal with: 1. The introduction, 2. Domains of linear fractional transformations, 3. Associated pairs of the first and second kind, 4. Matrix balls, 5. The classification of canonical systems via the limit ball, 6. The Weyl-Titchmarsh characterization of the input impedance, 7. Applications of interpolation to the bitangential inverse input impedance problem. Formulas for recovering the underlying canonical integral systems, examples and related results on the inverse bitangential spectral problem will be presented in subsequent publications.D. Z. Arov thanks the Weizmann Institute of Science for hospitality and support, partially as a Varon Visiting Professor and partially through the Minerva Foundation. H. Dym thanks Renee and Jay Weiss for endowing the chair which supports his research and the Minerva Foundation.  相似文献   

16.
矩阵有理插值及其误差公式   总被引:24,自引:1,他引:24  
矩阵有理插值及其误差公式顾传青,陈之兵(合肥工业大学)MATRIXVALUEDRATIONALINTERPOLANTSANDITSERRORFORMULA¥GuChuan-qing;ChenZhi-bing(HefeiUniversityofTech...  相似文献   

17.
A new method for the construction of bivariate matrix valued rational interpolants (BGIRI) on a rectangular grid is presented in [6]. The rational interpolants are of Thiele-type continued fraction form with scalar denominator. The generalized inverse introduced by [3]is gen-eralized to rectangular matrix case in this paper. An exact error formula for interpolation is ob-tained, which is an extension in matrix form of bivariate scalar and vector valued rational interpola-tion discussed by Siemaszko[l2] and by Gu Chuangqing [7] respectively. By defining row and col-umn-transformation in the sense of the partial inverted differences for matrices, two type matrix algorithms are established to construct corresponding two different BGIRI, which hold for the vec-tor case and the scalar case.  相似文献   

18.
The theory of the direct and bitangential inverse input impedance problem is used to solve the direct and bitangential inverse spectral problem. The analysis of the direct spectral problem uses and extends a number of results that appear in the literature. Special attention is paid to the class of canonical integral systems with matrizants that are strongly regular J-inner matrix valued functions in the sense introduced in [7]. The bitangential inverse spectral problem is solved in this class. In our considerations, the data for this inverse problem is a given nondecreasing p×p matrix valued function σ(μ) on and a normalized monotonic continuous chain of pairs , of entire inner p×p matrix valued functions. Each such chain defines a class of canonical integral systems in which we find a solution of the inverse problem for the given spectral function σ(μ). A detailed comparison of our investigations of inverse problems with those of Sakhnovich is presented.  相似文献   

19.
The general formulas developed in the fourth paper in this series are applied to solve the inverse input scattering problem for canonical integral systems in the special cases that the input scattering matrix is ap×q matrix valued function in the Wiener class (and the associated pairs are homogeneous). These formulas are then further specialized to the rational case. Whenp=q, these formulas are connected to the earlier results of Alpay-Gohberg and Gohberg-Kaashoek-Sakhnovich, who studied inverse problems for a related system of differential equations.This research was partially supported by a Minerva Foundation grant that is acknowledged with thanks.  相似文献   

20.
Bitangential input scattering problems are formulated and analyzed for canonical integral systems. Special attention is paid to the case when the input scattering matrix is ap×q matrix valued function of Wiener class. Formulas for the solution of the inverse input scattering problem are obtained by reproducing kernel Hilbert space methods. A number of illustrative examples are presented. Additional examples for the case when the input scattering matrix is of Wiener class/rational will be presented in a future publication.  相似文献   

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