• 제목/요약/키워드: Moore-Penrose matrix

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THE MOORE-PENROSE INVERSE OF THE PARTITIONED MARIX AND SIMULATION STUDY

  • Sunwoo, Ha-Sik
    • 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.

HIGHER ORDER ITERATIONS FOR MOORE-PENROSE INVERSES

  • Srivastava, Shwetabh;Gupta, D.K.
    • 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.

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

  • Deng, Chunyuan;Wei, Yimin
    • 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.

CONDITION NUMBERS WITH THEIR CONDITION NUMBERS FOR THE WEIGHTED MOORE-PENROSE INVERSE AND THE WEIGHTED LEAST SQUARES SOLUTION

  • Kang Wenhua;Xiang Hua
    • 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.

THE GENERALIZED WEIGHTED MOORE-PENROSE INVERSE

  • Sheng, Xingping;Chen, Guoliang
    • Journal of applied mathematics & informatics
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    • 제25권1_2호
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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.

COMPLETIONS OF HANKEL PARTIAL CONTRACTIONS OF SIZE 5×5 NON-EXTREMAL CASE

  • Lee, Sang Hoon
    • 충청수학회지
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    • 제29권1호
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    • pp.137-150
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    • 2016
  • We introduce a new approach that allows us to solve, algorithmically, the contractive completion problem. In this article, we provide concrete necessary and sufficient conditions for the existence of contractive completions of Hankel partial contractions of size $4{\times}4$ using a Moore-Penrose inverse of a matrix.

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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    • 제24권1_2호
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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.

무정보 blur 이미지 복구를 위한 DFT 변환 (A DFT Deblurring Algorithm of Blind Blur Image)

  • 문경일;김철
    • 정보교육학회논문지
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    • 제15권3호
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    • pp.517-524
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    • 2011
  • 어떠한 현상 혹은 사물의 이미지를 학생들에게 제공하는데 있어서 여러 가지 원인에 의해 초점이 흐리거나 혹은 흔들린 이미지들이 등장하여 학생들에게 보여주기가 힘든 경우가 빈번하게 발생한다. 특히, 이미지에 대한 구체적인 정보가 없는 경우에는 그 이미지는 쓸모가 없는 것이 된다. 본 연구는 무정보 블러링 이미지를 아주 빠른 시간 내에 복구할 수 있는 2차원 DFT 기반의 하나의 블러링 제거 알고리즘을 제안하는데 있다. 제안된 방법의 빠른 처리 속도는 이산 푸리에 변환, 변환의 필터링과 회선 관계 및 Moore-Penrose 역행렬의 효과적인 계산 방식을 바탕으로 한다. 특히, 필터의 주파수 응답에 관한 처리는 유용한 회선 공식을 유도한다. 제안된 방법의 구현은 보통 크기의 블러링 이미지에 적용했을 때, 아주 빠른 시간 내에 블러링 효과를 제거시킬 수 있고, 보다 선명한 이미지를 제공할 수 있음을 보인다.

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

  • 문창훈;한상을
    • 전산구조공학
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    • 제11권1호
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    • pp.217-226
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    • 1998
  • 본 논문은 변위제약모드를 갖는 트러스구조물의 형태해석을 목적으로 하였으며, 이를 위하여 해의 존재조건과 무어-펜로즈(Moore-Penrose) 일반역행렬을 이용하였다. 또한, 수치해석과정에서의 변위제약모드로는 호몰로지변형(homologous deformation)을 고려하여 해석하였고, 다음으로 다양한 변위제약모드와 절점에 작용하는 하중비를 만족하는 구조물의 형태를 구하였다. 본 논문에서의 형태해석문제는 지정된 변위를 만족하는 구조물의 형태를 찾는 일종의 역문제(inverse problem)로서 일반적인 구조해석과정과는 반대되는 입장에서 접근하였다. 또한, 본 논문에서는 수치해석과정에서 근사해의 정도를 향상시키기 위하여 뉴튼-랩슨법을 사용하였고, 수치해석예제로서 부재의 배열형태에 따라 3가지모델을 선택하였으며, 이들 모델을 통하여 적용한 해석기법의 정확성과 효율성을 검증하였다.

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