共查询到20条相似文献,搜索用时 15 毫秒
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K. C. Sivakumar 《Linear and Multilinear Algebra》2013,61(1):71-77
In this article we show that, contrary to finite matrices (with real or complex entries) an invertible infinite matrix V could have a Moore–Penrose inverse that is not a classical inverse of V. This also answers a recent open problem on infinite matrices. 相似文献
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Y. R. Hakopian A. N. Eloyan 《International Journal of Mathematical Education in Science & Technology》2013,44(8):1093-1102
As is known, a semi-magic square is an n?×?n matrix having the sum of entries in each row and each column equal to a constant. This note generalizes this notion and introduce a special class of block matrices called block magic rectangles. It is proved that the Moore–Penrose inverse of a block magic rectangle is also a block magic rectangle. 相似文献
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We prove a formula that relates the Moore–Penrose inverses of two matrices A,B such that A=N−1BM−1 and discuss some applications, in particular to the representation of the Moore–Penrose inverse of the normalized Laplacian of a graph. The Laplacian matrix of an undirected graph is symmetric and is strictly related to its connectivity properties. However, our formula applies to asymmetric matrices, so that we can generalize our results for asymmetric Laplacians, whose importance for the study of directed graphs is increasing. 相似文献
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Dijana Mosić 《Aequationes Mathematicae》2013,85(3):465-470
In this paper we give a positive solution to a conjecture on the reverse order law for the weighted Moore–Penrose inverse in C *-algebras (Mosi? and Djordjevi? in Electron. J. Linear Algebra 22:92–111, 2011). 相似文献
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In this article we study the existence of range projections in rings with involution, relating it to the existence of the Moore–Penrose inverse. The results are applied to the solution of the equation xbx?=?x in rings with involution, extending the results of Greville for matrices. Simpler new proofs are given of the Moore–Penrose invertibility of regular elements in rings with involution, and of the Ljance's formula. 相似文献
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We extend Rump’s verified method (S.Oishi, K.Tanabe, T.Ogita, S.M.Rump (2007)) for computing the inverse of extremely ill-conditioned square matrices to computing the Moore-Penrose inverse of extremely ill-conditioned rectangular matrices with full column (row) rank. We establish the convergence of our numerical verified method for computing the Moore-Penrose inverse. We also discuss the rank-deficient case and test some ill-conditioned examples. We provide our Matlab codes for computing the Moore-Penrose inverse. 相似文献
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A group of identities are established for the Moore–Penrose inverses and the weighted Moore–Penrose inverses of matrix products AB and ABC. Some consequences and applications are also presented. 相似文献
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A new method of solving the coefficient inverse problem 总被引:3,自引:0,他引:3
Ming-gen CUI Ying-zhen LIN & Li-hong YANG Department of Mathematics Harbin Institute of Technology Weihai China Department of Mathematics Harbin Institute of Technology Harbin China 《中国科学A辑(英文版)》2007,50(4):561-572
This paper is concerned with the new method for solving the coefficient inverse problem in the reproducing kernel space. It is different from the previous studies. This method gives accurate results and shows that it is valid by the numerical example. 相似文献
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A bi-block graph is a connected graph all of whose blocks are complete bipartite graphs. We give a combinatorial interpretation of the Moore–Penrose inverse of the incidence matrix of a complete multipartite graph and a bi-block graph. 相似文献
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The main objective of this article is to study several generalizations of the reverse order law for the Moore–Penrose inverse in ring with involution. 相似文献
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Abstract Orthodox semigroups have been studied by many authors, in particular by Hall, Yamada and Petrich. In this paper, we give the standard representation of orthodox semigroups and investigate various e-varieties of orthodox semigroups which are determined by the standard representations. 相似文献
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《Journal of Computational and Applied Mathematics》1986,16(3):343-354
This paper presents a new predictor–corrector method for finding a local minimum of a twice continuously differentiable function. The method successively constructs an approximation to the solution curve and determines a predictor on it using a technique similar to that used in trust region methods for unconstrained optimization. The proposed predictor is expected to be more effective than Euler's predictor in the sense that the former is usually much closer to the solution curve than the latter for the same step size. Results of numerical experiments are reported to demonstrate the effectiveness of the proposed method. 相似文献
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We develop a numerical method for computing with orthogonal polynomials that are orthogonal on multiple, disjoint intervals for which analytical formulae are currently unknown. Our approach exploits the Fokas–Its–Kitaev Riemann–Hilbert representation of the orthogonal polynomials to produce an method to compute the first N recurrence coefficients. The method can also be used for pointwise evaluation of the polynomials and their Cauchy transforms throughout the complex plane. The method encodes the singularity behavior of weight functions using weighted Cauchy integrals of Chebyshev polynomials. This greatly improves the efficiency of the method, outperforming other available techniques. We demonstrate the fast convergence of our method and present applications to integrable systems and approximation theory. 相似文献