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1.
本文中对HiIbert 空间中有界线性算子的带W-权Drazin 逆给出一个统一表示定理。並给出基于Newton插值和Hermite插值的计算Hilberφ空间有界线性算子 Drazin逆和带W-权Drazin 逆的两个迭代法、並给出了渐近误差界。 数值例子表明,矩阵的带W-权Draxin逆可以用这两个迭代法计算,並且后一种方法收敛速度快于前一种方法。  相似文献   

2.
关于长方矩阵加权Drazin逆的一种分裂法   总被引:4,自引:0,他引:4  
本文给出了求解长方矩阵加W-权Drazin逆的一种分裂法及其相应的迭代法;并且讨论了迭代法收敛到加W-权Drazin逆的充分必要条件。对迭代法半收敛的情形,本文亦作了讨论。  相似文献   

3.
本文利用正交投影算子分块形式的表示式,给出了两个投影算子P,Q乘积的MoorePenrose逆以及Drazin逆的表示,并利用所得结果给出了P,Q乘积Drazin逆的相关等式和性质.最后得到了投影算子P,Q的Moore-Penrose逆以及Drazin逆反序律之间的等价关系.  相似文献   

4.
线性算子的DRAZIN广义逆   总被引:1,自引:0,他引:1  
在[1]中,乔三正在 Banach 空间中讨论了线性算子的 Drazin 广义逆的存在条件,并得出了 Drazin 逆的一系列性质。在[2]中,匡蛟勋在 Hilbert 空间给出了某一类算子的Drazin 逆的一个统一的表示定理,并由它导出一系列不同的迭代格式.本文在向量空间中讨论了 Drazin 逆存在的充分必要条件,并具体给出了 Drazin 逆的一个明确的表达形式,它将求 Drazin 逆的问题化为求加号逆的问题,而对求加号逆已有很多已知的方法(见[3],[4]),因此这个表达形式对求解 Drazin 带来极大的方便。当空间为完备的不变度量 d 诱导的拓扑向量空间时(即 X 为 F—空间时),我们讨论了连续Drazin 逆存在的充分必要条件.在 Banach 空间给出了一个 Drazin 逆的表示定理.特别  相似文献   

5.
1981年,1985年,2000年,乔三正、蔡东汉、魏益民分别给出Drazin广义逆不同形式的表示.本文将对上述结果进行推广,给出Drazin广义逆的统一表示,使上述三个结果均成为本文主要结果的特例.在本文主要结果的基础上,利用算子谱理论,给出Drazin广义逆的一种逼近形式的表示,同时给出逼近解的估计.此结果推广了蔡东汉、魏益民的相应结果.  相似文献   

6.
Hilbert空间中算子广义逆的积分表示   总被引:2,自引:0,他引:2  
利用算子矩阵分块的技巧,得到了Hilbert空间中算子的Moore-Penrose逆和Drazin逆的积分表示.给出了较为简洁的证明,同时将有限维的结论推广到无限维的情形.  相似文献   

7.
利用矩阵A的带W权Drazin逆的一个性质特征,对任意的矩阵A∈Cm×n,W∈Cn×m,建立了带W权的Drazin逆Ad,w的一种新的表示式,给出了具体的算法步骤,并且在文末给出了算例.  相似文献   

8.
本文讨论了反三角算子矩阵■的Drazin可逆性及其Drazin逆的表达式.在CB=CAB=CA~2B,A~3=A~2条件下,采用预解式的Laurent展开方法证明了反三角算子矩阵M是Drazin可逆的,并给出M的含有A~D和(CB)~D的Drazin逆的表达式.最后给出算例,说明了结果的有效性.  相似文献   

9.
本文研究了两个有界线性算子和的Drazin逆的问题.利用算子的预解式展开的方法,得到了(P+Q)~D的具体表达式,并将其应用到四分块算子矩阵M=[A B C D]的Drazin逆上,推广了文献[14,15]的结果.  相似文献   

10.
讨论Banach空间中有界线性算子的Drazin逆的扰动问题.利用Jiu Ding在2003年给出的广义Neumann引理,给出关于Drazin逆的一个新扰动定理,并给出误差估计,推广了文献中相应的扰动结果.  相似文献   

11.
In this article, we study the reduced minimum modulus of the Drazin inverse of an operator on a Hilbert space and give lower and upper bounds of the reduced minimum modulus of an operator and its Drazin inverse, respectively. Using these results, we obtain a characterization of the continuity of Drazin inverses of operators on a Hilbert space.

  相似文献   


12.
This paper studies the integral representation of the W-weighted Drazin inverse for bounded linear operators between Hilbert spaces. By using operator matrix blocks, some integral representations of the W-weighted Drazin inverse for Hilbert space operators are established.  相似文献   

13.
To study singular linear system, Cline and Greville[8] proposed the concept of W-weighted Drazin inverse for the rectangular matrices,where the properties were also discussed. The computation for the W-weighted Drazin inverse is of much interest, which is mainly divided into two kinds of methods: direct method[2,4,6] and iterative method[3,5,7,9,12,13]. In this paper, we study the iterative method and successive matrix squaring(SMS) method for the W-weighted Drazin inverse and generalize the main results in [12,13].  相似文献   

14.
LetA andE bem x n matrices andW an n xm matrix, and letA d,W denote the W-weighted Drazin inverse ofA. In this paper, a new representation of the W-weighted Drazin inverse ofA is given. Some new properties for the W-weighted Drazin inverseA d,W and Bd,W are investigated, whereB =A+E. In addition, the Banach-type perturbation theorem for the W-weighted Drazin inverse ofA andB are established, and the perturbation bounds for ∥Bd,W∥ and ∥Bd, W, -Ad,W∥/∥Ad,W∥ are also presented. WhenA andB are square matrices andW is identity matrix, some known results in the literature related to the Drazin inverse and the group inverse are directly reduced by the results in this paper as special cases.  相似文献   

15.
A new binary relation associated with the core–EP inverse is presented and studied on the corresponding subset of all generalized Drazin invertible bounded linear Hilbert space operators. Using the (dual) core partial order between core parts of operators and the minus partial order between quasinilpotent parts of operators, new pre-orders and partial orders are also introduced and characterized.  相似文献   

16.
In this paper we study the W-weighted Drazin inverse of the bounded linear operators between Banach spaces and its representation theorem. Based on this representation, utilizing the spectral theory of Banach space operators, we derive an approximating expression of the W-weighted Drazin inverse and an error bound. Also, a perturbation theorem for the W-weighted Drazin inverse is uniformly obtained from the representation theorem.  相似文献   

17.
In this note, some equivalents are established of the Drazin invertibility of differences and sums of idempotent operators on a Hilbert space.  相似文献   

18.
In this paper, we define and study the left and the right generalized Drazin inverse of bounded operators in a Banach space. We show that the left (resp. the right) generalized Drazin inverse is a sum of a left invertible (resp. a right invertible) operator and a quasi-nilpotent one. In particular, we define the left and the right generalized Drazin spectra of a bounded operator and also show that these sets are compact in the complex plane and invariant under additive commuting quasi-nilpotent perturbations. Furthermore, we prove that a bounded operator is left generalized Drazin invertible if and only if its adjoint is right generalized Drazin invertible. An equivalent definition of the pseudo-Fredholm operators in terms of the left generalized Drazin invertible operators is also given. Our obtained results are used to investigate some relationships between the left and right generalized Drazin spectra and other spectra founded in Fredholm theory.  相似文献   

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