不变子空间上特征值的扰动

1引言设矩阵A∈C~(n×n),B∈C~(m×m),Q∈C~(n×m)为列满秩矩阵,令R=AQ-QB．当R的范数很小的时候,我们分析矩阵B的特征值对A的特征值的逼近性．当A,B都是Hermite阵时,上述问题已经被Kahan解决．近年来,对可对角化矩阵的情形,取得了一些新的成果．[4][5][6]中给出了几个范数不等式,并应用于矩阵特征值     

CONDITION NUMBERS OF A MULTIPLE EIGENVALUE

This paper studies the symmetric eigenvalue problem Ax = λBx, where A,B are real symmetric matrices, and B is positive definite. Condition numbers of a multiple eigenvalue are derived from the first order perturbation expansions.     

关于不变平行闭子空间的一个注记

利用完全正映射与相似 同态问题的关系 ,给出了满足特殊条件具有相同算子值的两个算子 ,其值关于算子系为不变的一个等价条件     

MULTIPLICATION OPERATORS ON INVARIANT SUBSPACES OF FUNCTION SPACES

Let M? be the operator of multiplication by?on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral prope...     

代数Riccati方程可稳解的条件数

１．引言 关于代数Ｒｉｃｃａｔｉ方程（ＡＲＥ）的研究是大量的．从数值角度看,有关数值方法,扰动理论的研究已比较深入．而关于条件数理论的研究则还不多［３］,［６］． Ｒｙｅｒｓ［１］研究了时连续代数 Ｒｉｃｃａｔｉ方程可稳解的条件数; Ｋｅｎｎｅｙ和 Ｈｅｗｅｒ［３］讨论了时连续代数 Ｒｉｃｃａｔｉ方程（以下简称 ＣＴＡＲＥ）可稳解的敏度分析,给出了一阶扰动界,引进了条件数; Ｓｕｎ［６］从最佳向后扰动理论角度研究了时离散代数Ｒｉｃｃａｔｉ方程（以下简称ＤＴＡＲＥ）可稳解的条件数;徐树方［８］针对 ＣＴＡ…     

MATRIX NORM VERSIONS OF THE KANTOROVICH INEQUALITY AND ITS APPLICATIONS

In this paper we discuss the generalizations of the Kantorovich inequality and obtain some generalized Kantorovich inequalities in the sense of matrix norm. We further illustrate how to use these inequalities to determine the lower bound of relative efficiency of the parameter estimate in linear model.     

THE MINIMAL PROPERTY OF THE CONDITION NUMBER OF INVERTIBLE LINEAR BOUNDED OPERATORS IN BANACH SPACES

In this paper we show that in error estimates, the condition number k(T) of any in-vertible linear bounded operator T in Banach spaces is minimal. We also extend the Hahn-Ba-nach theorem and other related results.     

一阶HÖlder条件下带参数的修正型Euler-Halley迭代族的局部收敛性

1引言设X和Y为实或复Banach空间,Ω■X是开凸子集,F:Ω■X→Y是一阶连续可微的非线性算子.非线性算子方程F(x)=0 (1.1) 的求解及收敛域问题是现代科学计算理论的基本问题.解方程(1.1)的最著名的迭代方法是Newton法,在适当的条件下,它是二阶收敛的,此即著名的Kantorovich定理.关于Newton法收敛球半径的估计由Traub和王兴华分别给出,见[2]和[3],而收敛性研究的进一步发展可参看[4,5,6]及综述文章[7].