• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.81-96
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• 2004

The level-m scaled circulant factor matrix over the complex number field is introduced. Its diagonalization and spectral decomposition and representation are discussed. An explicit formula for the entries of the inverse of a level-m scaled circulant factor matrix is presented. Finally, an algorithm for finding the inverse of such matrices over the quaternion division algebra is given.

• Journal of the Korean Data and Information Science Society
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• 제23권5호
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• pp.1027-1035
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• 2012

This paper proposes a new Levenberg-Marquardt algorithm that is accelerated by adjusting a Jacobian matrix and a quasi-Hessian matrix. The proposed method partitions the Jacobian matrix into block matrices and employs the inverse of a partitioned matrix to find the inverse of the quasi-Hessian matrix. Our method can avoid expensive operations and save memory in calculating the inverse of the quasi-Hessian matrix. It can shorten the training time for fast convergence. In our results tested in a large application, we were able to save about 20% of the training time than other algorithms.

• 대한기계학회논문집A
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• 제22권1호
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• pp.170-176
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• 1998

In this paper, the column space and null space of the Jacobian matrix were obtained by using the pseudo-inverse method and projection matrix. The equations of motion of the system were replaced by independent acceleration components using the null space matrix. The proposed method has the following advantages. (1) It is simple to derive the null space. (2) The efficiency is improved by getting rid of constrained force terms. (3) Neither null space updating nor coordinate partitioning method is required. The suggested algorithm is applied to a three-dimensional vehicle model to show the efficiency.

• ETRI Journal
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• 제39권6호
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• pp.841-850
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• 2017

We investigate neural network image reconstruction for magnetic particle imaging. The network performance strongly depends on the convolution effects of the spectrum input data. The larger convolution effect appearing at a relatively smaller nanoparticle size obstructs the network training. The trained single-layer network reveals the weighting matrix consisting of a basis vector in the form of Chebyshev polynomials of the second kind. The weighting matrix corresponds to an inverse system matrix, where an incoherency of basis vectors due to low convolution effects, as well as a nonlinear activation function, plays a key role in retrieving the matrix elements. Test images are well reconstructed through trained networks having an inverse kernel matrix. We also confirm that a multi-layer network with one hidden layer improves the performance. Based on the results, a neural network architecture overcoming the low incoherence of the inverse kernel through the classification property is expected to become a better tool for image reconstruction.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.113-126
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• 2007

Let A and E be $m{\times}n$ matrices and W an $n{\times}m$ matrix, and let $A_{d,w}$ denote the W-weighted Drazin inverse of A. In this paper, a new representation of the W-weighted Drazin inverse of A is given. Some new properties for the W-weighted Drazin inverse $A_{d,w}\;and\;B_{d,w}$ are investigated, where B=A+E. In addition, the Banach-type perturbation theorem for the W-weighted Drazin inverse of A and B are established, and the perturbation bounds for ${\parallel}B_{d,w}{\parallel}\;and\;{\parallel}B_{d,w}-A_{d,w}{\parallel}/{\parallel}A_{d,w}{\parallel}$ are also presented. When A and B are square matrices and W is identity matrix, some known results in the literature related to the Drazin inverse and the group inverse are directly reduced by the results in this paper as special cases.

• 충청수학회지
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• 제25권4호
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• pp.609-615
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• 2012

In the current paper, we establish the relationship between the powers of an invertible matrix and the powers of its inverse. More precisely, we prove that if A is an invertible matrix and, if $A^n\;=\;(A_{i,j}(n))$ for all positive integer n, then $A^{-n}\;=\;(A_{i,j}{(-n))$.

• 대한기계학회논문집B
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• 제30권3호
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• pp.270-277
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• 2006

Inverse radiation problems were solved for estimating boundary temperature distribution in a way of function estimation approach in an axisymmetric absorbing, emitting and scattering medium, given the measured radiative data. In order to reduce the computational time fur the calculation of sensitivity matrix, automatic differentiation and Broyden combined method were adopted, and their computational precision and efficiency were compared with the result obtained by finite difference approximation.. In inverse analysis, the effects of the precision of sensitivity matrix, the number of measurement points and measurement error on the estimation accuracy had been inspected using quasi-Newton method as an inverse method. Inverse solutions were validated with the result acquired by additional inverse methods of conjugate-gradient method or Levenberg-Marquardt method.

• 대한인간공학회지
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• 제14권2호
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• pp.33-39
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• 1995

The inverse Kinematics can be used for representing the motion of human body model. In order to find the final figure of the human body model with given target position, we can uwe the formula x=J .THETA. , where J is the Jacobian matrix of x=f( .THETA.), of the Inverse Kinematics. In this formula, f has so complicated form that it is difficult to calcuate the Jacobian matrix J by expanding all formulae exactly. In this paper, a numerical method that calculates the Jacobian matrix is proosed. The simulation results obtained by using the simple human model reprsent that the proposed. The simulation results obtained by using the simple human model represent that the proposed method is useful for generating the final figure of the body model.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 춘계학술대회논문집
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• pp.997-1002
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• 2001

This paper describes an implementation of inverse filter using SVD in order to recover the input in multi-channel system. The matrix formulation in SISO system is extended to MIMO system. In time and frequency domain we investigates the inversion of minimum phase system and non-minimum phase system. To execute an effective inversion of non-minimum phase system, SVD is introduced. First of all we computes singular values of system matrix and then investigates the phase property of system. In case of overall system is non-minimum phase, system matrix has one (or more) very small singular value(s). The very small singular value(s) carries information about phase properties of system. Using this property, approximate inverse filter of overall system is founded. The numerical simulation shows potentials in use of the inverse filter.

• 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.