共查询到20条相似文献,搜索用时 598 毫秒
1.
Predrag S. Stanimirović N. P. Karampetakis Milan B. Tasić 《Journal of Applied Mathematics and Computing》2007,24(1-2):81-94
In this paper we investigate symbolic implementation of two modifications of the Leverrier-Faddeev algorithm, which are applicable in computation of the Moore-Penrose and the Drazin inverse of rational matrices. We introduce an algorithm for computation of the Drazin inverse of rational matrices. This algorithm represents an extension of the papers [11] and [14]. and a continuation of the papers [15, 16]. The symbolic implementation of these algorithms in the package mathEmatica is developed. A few matrix equations are solved by means of the Drazin inverse and the Moore-Penrose inverse of rational matrices. 相似文献
2.
In this paper,we give further results on the Drazin inverse of tensors via the Einstein product.We give a limit formula for the Drazin inverse of tensors.By using this formula,the representations for the Drazin inverse of several block tensor are obtained.Further,we give the Drazin inverse of the sum of two tensors based on the representation for the Drazin inverse of a block tensor. 相似文献
3.
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
4.
Guo-Rong Wang 《计算数学(英文版)》1990,8(4):353-362
This paper deals with a system of ordinary differential equations with known conditions associated with a given matrix. By using analytical and computational methods, the generalized inverses of the given matrix can be determined. Among these are the weighted Moore-Penrose inverse, the Moore-Penrose inverse, the Drazin inverse and the group inverse. In particular, a new insight is provided into the finite algorithms for computing the generalized inverse and the inverse. 相似文献
5.
We introduce new expressions for the generalized Drazin inverse of a block matrix with the generalized Schur complement being generalized Drazin invertible in a Banach algebra under some conditions. We generalized some recent results for Drazin inverse and group inverse of complex matrices. 相似文献
6.
§ 1.Introduction In [1 ],theauthordefinedaccuratelytheDrazininverseofamorphism .Previously ,somenecessaryandsufficientconditionswereobtainedforamorphismwith (epic ,monic)factorizationtohavethegroupinverse (see [2 ],Theorem 1 )andtheDrazininverseofamatrixoverthecomp… 相似文献
7.
态射的Drazin逆 总被引:10,自引:1,他引:10
本文研究范畴中态射的Drazin逆.给出了一般范畴中态射的{1m,2,5}逆的一个等价刻划.在Abel范畴中,建立指数与Drazin逆的概念,证明了有Drazin逆的态射必有柱心-幂零分解. 相似文献
8.
0truemm0truemm We study properties of elements in a ring which admit the generalized Drazin inverse. It is shown that the element 1-ab is generalized Drazin invertible if and only if so is 1-ba and a formula for the generalized Drazin inverse of 1-ba in terms of the generalized Drazin inverse and the spectral idempotent of 1-ab is provided. Further, recent results relating to the Drazin index can be recovered from our theorems. 相似文献
9.
Konstantin E. Avrachenkov Jean B. Lasserre 《Linear algebra and its applications》2013,438(4):1793-1813
We investigate the analytic perturbation of generalized inverses. Firstly we analyze the analytic perturbation of the Drazin generalized inverse (also known as reduced resolvent in operator theory). Our approach is based on spectral theory of linear operators as well as on a new notion of group reduced resolvent. It allows us to treat regular and singular perturbations in a unified framework. We provide an algorithm for computing the coefficients of the Laurent series of the perturbed Drazin generalized inverse. In particular, the regular part coefficients can be efficiently calculated by recursive formulae. Finally we apply the obtained results to the perturbation analysis of the Moore–Penrose generalized inverse in the real domain. 相似文献
10.
A characterization of nonnegative matrices which have a nonnegative Drazin inverse is given. A necessary and sufficient condition for a real matrix to have a nonnegative Drazin inverse is also presented. 相似文献
11.
高璟 《数学的实践与认识》2007,37(7):125-128
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
12.
Starting from algorithms introduced in [Ky M. Vu, An extension of the Faddeev’s algorithms, in: Proceedings of the IEEE Multi-conference on Systems and Control on September 3-5th, 2008, San Antonio, TX] which are applicable to one-variable regular polynomial matrices, we introduce two dual extensions of the Faddeev’s algorithm to one-variable rectangular or singular matrices. Corresponding algorithms for symbolic computing the Drazin and the Moore-Penrose inverse are introduced. These algorithms are alternative with respect to previous representations of the Moore-Penrose and the Drazin inverse of one-variable polynomial matrices based on the Leverrier-Faddeev’s algorithm. Complexity analysis is performed. Algorithms are implemented in the symbolic computational package MATHEMATICA and illustrative test examples are presented. 相似文献
13.
A weighted Drazin inverse and applications 总被引:5,自引:0,他引:5
In this paper the notation of the Cline–Greville W-weighted Drazin inverse of a rectangular matrix is extended to bounded linear operators between Banach spaces. We give new characterizations of the W-weighted Drazin inverse, and we study the perturbations and the the continuity of the W-weighted Drazin inverse. 相似文献
14.
In order to estimate error bounds on the computed Drazin inverse of a matrix, we need to establish some perturbation theory for the Drazin inverse which is analogous to that for the Moore–Penrose inverse. In this paper, we present recent results on this topic, three problems are put forward in this direction. 相似文献
15.
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
16.
Jelena Ljubisavljevi?Dragana S. Cvetkovi?-Ili? 《Journal of Computational and Applied Mathematics》2011,235(12):3683-3690
In this paper, we consider the Drazin inverse of a sum of two matrices and derive additive formulas under conditions weaker than those used in some recent papers on the subject. As a corollary we get the main results from the paper of Yang and Liu [H. Yang, X. Liu, The Drazin inverse of the sum of two matrices and its applications, J. Comput. Appl. Math. 235 (2011) 1412-1417]. As an application we give some new representations for the Drazin inverse of a block matrix. 相似文献
17.
Israr Ali Khan 《Linear and Multilinear Algebra》2013,61(9):1019-1029
In this article, we investigate the Drazin invertibility for the elements of an arbitrary semiring. We give necessary and sufficient conditions for the existence and expressions of the Drazin inverse of an element in an arbitrary semiring. Moreover, we consider the product paq under some additional necessary conditions for which the Drazin inverse of the product paq exists. 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
19.
Aleksandar S. Cvetkovi? Gradimir V. Milovanovi? 《Journal of Mathematical Analysis and Applications》2011,375(1):331-335
In this short paper, we offer (another) formula for the Drazin inverse of an operator matrix for which certain products of the entries vanish. We also give formula for the Drazin inverse of the sum of two operators under special conditions. 相似文献
20.
卜凡斌 《高等学校计算数学学报》2004,26(2):97-109
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