• Title/Summary/Keyword: Moore-Penrose Generalized inverse

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MOORE-PENROSE INVERSE IN AN INDEFINITE INNER PRODUCT SPACE

  • KAMARAJ K.;SIVAKUMAR K. C.
    • Journal of applied mathematics & informatics
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    • v.19 no.1_2
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    • pp.297-310
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    • 2005
  • The concept of the Moore-Penrose inverse in an indefinite inner product space is introduced. Extensions of some of the formulae in the Euclidean space to an indefinite inner product space are studied. In particular range-hermitianness is completely characterized. Equivalence of a weighted generalized inverse and the Moore-Penrose inverse is proved. Finally, methods of computing the Moore-Penrose inverse are presented.

THE GENERALIZED WEIGHTED MOORE-PENROSE INVERSE

  • Sheng, Xingping;Chen, Guoliang
    • Journal of applied mathematics & informatics
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    • v.25 no.1_2
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    • pp.407-413
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    • 2007
  • In this paper, we definite a generalized weighted Moore-Penrose inverse $A^{+}_{M,N}$ of a given matrix A, and give the necessary and sufficient conditions for its existence. We also prove its uniqueness and give a representation of it. In the end we point out this generalized inverse is also a prescribed rang T and null space S of {2}-(or outer) inverse of A.

WEIGHTED GDMP INVERSE OF OPERATORS BETWEEN HILBERT SPACES

  • Mosic, Dijana
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.4
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    • pp.1263-1271
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    • 2018
  • We introduce new generalized inverses (named the WgDMP inverse and dual WgDMP inverse) for a bounded linear operator between two Hilbert spaces, using its Wg-Drazin inverse and its Moore-Penrose inverse. Some new properties of WgDMP inverse and dual WgDMP inverse are obtained and some known results are generalized.

PERTURBATION ANALYSIS OF THE MOORE-PENROSE INVERSE FOR A CLASS OF BOUNDED OPERATORS IN HILBERT SPACES

  • Deng, Chunyuan;Wei, Yimin
    • Journal of the Korean Mathematical Society
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    • v.47 no.4
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    • pp.831-843
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    • 2010
  • Let $\cal{H}$ and $\cal{K}$ be Hilbert spaces and let T, $\tilde{T}$ = T + ${\delta}T$ be bounded operators from $\cal{H}$ into $\cal{K}$. In this article, two facts related to the perturbation bounds are studied. The first one is to find the upper bound of $\parallel\tilde{T}^+\;-\;T^+\parallel$ which extends the results obtained by the second author and enriches the perturbation theory for the Moore-Penrose inverse. The other one is to develop explicit representations of projectors $\parallel\tilde{T}\tilde{T}^+\;-\;TT^+\parallel$ and $\parallel\tilde{T}^+\tilde{T}\;-\;T^+T\parallel$. In addition, some spectral cases related to these results are analyzed.

Parameter Optimization of Extreme Learning Machine Using Bacterial Foraging Algorithm (Bacterial Foraging Algorithm을 이용한 Extreme Learning Machine의 파라미터 최적화)

  • Cho, Jae-Hoon;Lee, Dae-Jong;Chun, Myung-Geun
    • Journal of the Korean Institute of Intelligent Systems
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    • v.17 no.6
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    • pp.807-812
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    • 2007
  • Recently, Extreme learning machine(ELM), a novel learning algorithm which is much faster than conventional gradient-based learning algorithm, was proposed for single-hidden-layer feedforward neural networks. The initial input weights and hidden biases of ELM are usually randomly chosen, and the output weights are analytically determined by using Moore-Penrose(MP) generalized inverse. But it has the difficulties to choose initial input weights and hidden biases. In this paper, an advanced method using the bacterial foraging algorithm to adjust the input weights and hidden biases is proposed. Experiment at results show that this method can achieve better performance for problems having higher dimension than others.

A Study on the Shape Analysis Method of Plane Truss Structures under the Prescribed Displacement (변위제약을 받는 평면트러스 구조물의 형태해석기법에 관한 연구)

  • 문창훈;한상을
    • Computational Structural Engineering
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    • v.11 no.1
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    • pp.217-226
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    • 1998
  • The purpose of this study is to develop a technique for the shape analysis of plane truss structures under prescribed displacement modes. The shape analysis is performed based on the existence theorem of the solution and the Moore-Penrose generalized inverse matrix. In this paper, the homologous deformation of structures was proposed as prescribed displacement modes, the shape of the structure is determined from these various modes and applied loads. In general, the shape analysis is a kind of inverse problem different from stress analysis, and the governing equation becomes nonlinear. In this regard, Newton-Raphson method was used to solve the nonlinear equation. Three different shape models are investigated as numerical examples to show the accuracy and the effectiveness of the proposed method.

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COMPUTING GENERALIZED INVERSES OF A RATIONAL MATRIX AND APPLICATIONS

  • Stanimirovic, Predrag S.;Karampetakis, N. P.;Tasic, Milan B.
    • Journal of applied mathematics & informatics
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    • v.24 no.1_2
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    • pp.81-94
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    • 2007
  • 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.

SINGULAR INTEGRAL EQUATIONS AND UNDERDETERMINED SYSTEMS

  • KIM, SEKI
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.2 no.2
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    • pp.67-80
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    • 1998
  • In this paper the linear algebraic system obtained from a singular integral equation with variable coeffcients by a quadrature-collocation method is considered. We study this underdetermined system by means of the Moore Penrose generalized inverse. Convergence in compact subsets of [-1, 1] can be shown under some assumptions on the coeffcients of the equation.

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Dynamic analysis of deployable structures using independent displacement modes based on Moore-Penrose generalized inverse matrix

  • Xiang, Ping;Wu, Minger;Zhou, Rui Q.
    • Structural Engineering and Mechanics
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    • v.54 no.6
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    • pp.1153-1174
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    • 2015
  • Deployable structures have gained more and more applications in space and civil structures, while it takes a large amount of computational resources to analyze this kind of multibody systems using common analysis methods. This paper presents a new approach for dynamic analysis of multibody systems consisting of both rigid bars and arbitrarily shaped rigid bodies. The bars and rigid bodies are connected through their nodes by ideal pin joints, which are usually fundamental components of deployable structures. Utilizing the Moore-Penrose generalized inverse matrix, equations of motion and constraint equations of the bars and rigid bodies are formulated with nodal Cartesian coordinates as unknowns. Based on the constraint equations, the nodal displacements are expressed as linear combination of the independent modes of the rigid body displacements, i.e., the null space orthogonal basis of the constraint matrix. The proposed method has less unknowns and a simple formulation compared with common multibody dynamic methods. An analysis program for the proposed method is developed, and its validity and efficiency are investigated by analyses of several representative numerical examples, where good accuracy and efficiency are demonstrated through comparison with commercial software package ADAMS.