• Journal of applied mathematics & informatics
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• 제5권3호
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• pp.849-857
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• 1998

In this paper we have a concern on the Moore-Penrose inverse of two kinds of partitioned matrices of the form [V X] and [{{{{ {V atop {X} {{{{ {X atop { 0} }}] where V is symmetric. The Moore-Penrose inverse of the partitioned matrices can be reduced to be simpler forms according to some algebraic conditions. Firstly we investigate the representations of the Moore-Penrose inverses of the partitioned matrices under four al-gebraic conditions. Each condition reduces the Moore-Penrose inverses of the partitioned matrices under four al-gebraic conditions. Each condition reduces the Morre-Penrose inverse into some simpler form. Also equivalant conditions will be considered. Finally we will perform a simulation study to investigate which con-dition is the most important in the sense that which condition occurs the most frequently in the real situation. The simluation study will show us a particular condition occurs the most likely tha other conditions. This fact enables us to obtain the Morre-Penrose inverse with less computational efforts and computational storage.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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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.

• 대한수학회보
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• 제51권2호
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• pp.501-510
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• 2014

We characterize hypergeneralized k-projectors (i.e., $A^k=A^{\dag}$). Also, some representation for the Moore-Penrose inverse of a linear combination of hypergeneralized k-projectors is found and the invertibility for some linear combinations of commuting hypergeneralized k-projectors is considered.

• 대한수학회지
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• 제57권3호
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• pp.691-706
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• 2020

Necessary and sufficient conditions are provided under which the weighted Moore-Penrose inverse A^†_MN exists, where A is an adjointable operator between Hilbert C^⁎-modules, and the weights M and N are only self-adjoint and invertible. Relationship between weighted Moore-Penrose inverses A^†_MN is clarified when A is fixed, whereas M and N are variable. Perturbation analysis for the weighted Moore-Penrose inverse is also provided.

• 대한수학회지
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• 제46권6호
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• pp.1139-1150
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• 2009

We obtain necessary and sufficient conditions for $2{\tims}2$ block operator valued matrices to be Moore-Penrose (MP) invertible and give new representations of such MP inverses in terms of the individual blocks.

• 대한수학회지
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• 제50권6호
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• pp.1349-1367
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• 2013

The weighted Moore-Penrose inverse will be introduced and studied in the context of Banach algebras. In addition, weighted EP Banach algebra elements will be characterized. The Banach space operator case will be also considered.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.171-184
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• 2014

A higher order iterative method to compute the Moore-Penrose inverses of arbitrary matrices using only the Penrose equation (ii) is developed by extending the iterative method described in [1]. Convergence properties as well as the error estimates of the method are studied. The efficacy of the method is demonstrated by working out four numerical examples, two involving a full rank matrix and an ill-conditioned Hilbert matrix, whereas, the other two involving randomly generated full rank and rank deficient matrices. The performance measures are the number of iterations and CPU time in seconds used by the method. It is observed that the number of iterations always decreases as expected and the CPU time first decreases gradually and then increases with the increase of the order of the method for all examples considered.

• 한국지능시스템학회논문지
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• 제17권6호
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• pp.807-812
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• 2007

최근 단일 은닉층을 갖는 전방향 신경회로망 구조로, 기존의 경사 기반 학습알고리즘들보다 학습 속도가 매우 우수한 ELM(Extreme Learning Machine)이 제안되었다. ELM 알고리즘은 입력 가중치들과 은닉 바이어스들의 초기 값을 무작위로 선택하고 출력 가중치들은 Moore-Penrose(MP) 일반화된 역행렬 방법을 통하여 구해진다. 그러나 입력 가중치들과 은닉층 바이어스들의 초기 값 선택이 어렵다는 단점을 갖고 있다. 본 논문에서는 최적화 알고리즘 중 박테리아 생존(Bacterial Foraging) 알고리즘의 수정된 구조를 이용하여 ELM의 초기 입력 가중치들과 은닉층 바이어스들을 선택하는 개선된 방법을 제안하였다. 실험을 통하여 제안된 알고리즘이 많은 입력 데이터를 가지는 문제들에 대하여 성능이 우수함을 보였다.

• 대한수학회지
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• 제47권4호
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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.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.95-112
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• 2006

In this paper, the authors investigate the condition number with their condition numbers for weighted Moore-Penrose inverse and weighted least squares solution of min /Ax - b/M, where A is a rank-deficient complex matrix in $C^{m{\times}n} $ and b a vector of length m in $C^m$, x a vector of length n in $C^n$. For the normwise condition number, the sensitivity of the relative condition number itself is studied, the componentwise perturbation is also investigated.