• Title, Summary, Keyword: inverse problem

### INVERSE CONSTRAINED MINIMUM SPANNING TREE PROBLEM UNDER HAMMING DISTANCE

• Jiao, Li;Tang, Heng-Young
• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.283-293
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• 2010
• In this paper, inverse constrained minimum spanning tree problem under Hamming distance. Such an inverse problem is to modify the weights with bound constrains so that a given feasible solution becomes an optimal solution, and the deviation of the weights, measured by the weighted Hamming distance, is minimum. We present a strongly polynomial time algorithm to solve the inverse constrained minimum spanning tree problem under Hamming distance.

### Analysis of an Inverse Heat Conduction Problem Using Maximum Entropy Method (최대엔트로피법을 이용한 역열전도문제의 해석)

• Kim, Sun-Kyoung;Lee, Woo-Il
• Proceedings of the KSME Conference
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• pp.144-147
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• 2000
• A numerical method for the solution of one-dimensional inverse heat conduction problem is established and its performance is demonstrated with computational results. The present work introduces the maximum entropy method in order to build a robust formulation of the inverse problem. The maximum entropy method finds the solution that maximizes the entropy functional under given temperature measurement. The philosophy of the method is to seek the most likely inverse solution. The maximum entropy method converts the inverse problem to a non-linear constrained optimization problem of which constraint is the statistical consistency between the measured temperature and the estimated temperature. The successive quadratic programming facilitates the maximum entropy estimation. The gradient required fur the optimization procedure is provided by solving the adjoint problem. The characteristic feature of the maximum entropy method is discussed with the illustrated results. The presented results show considerable resolution enhancement and bias reduction in comparison with the conventional methods.

### THE SOLVABILITY CONDITIONS FOR A CLASS OF CONSTRAINED INVERSE EIGENVALUE PROBLEM OF ANTISYMMETRIC MATRICES

• PAN XIAO-PING;HU XI-YAN;ZHANG LEI
• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.87-98
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• 2006
• In this paper, a class of constrained inverse eigenvalue problem for antisymmetric matrices and their optimal approximation problem are considered. Some sufficient and necessary conditions of the solvability for the inverse eigenvalue problem are given. A general representation of the solution is presented for a solvable case. Furthermore, an expression of the solution for the optimal approximation problem is given.

### A TRACE-TYPE FUNCTIONAL METHOD FOR DETERMINATION OF A COEFFICIENT IN AN INVERSE HEAT CONDUCTION PROBLEM

• WEN, JIN;CHENG, JUN-FENG
• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.439-447
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• 2017
• This paper investigates the inverse problem of determining an unknown heat radiative coefficient, which is only time-dependent. This is an ill-posed problem, that is, small errors in data may cause huge deviations in determining solution. In this paper, the existence and uniqueness of the problem is established by the second Volterra integral equation theory, and the method of trace-type functional formulation combined with finite difference scheme is studied. One typical numerical example using the proposed method is illustrated and discussed.

### Inverse Bin-Packing Number Problems: Polynomially Solvable Cases

• Chung, Yerim
• Management Science and Financial Engineering
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• v.19 no.1
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• pp.25-28
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• 2013
• Consider the inverse bin-packing number problem. Given a set of items and a prescribed number K of bins, the inverse bin-packing number problem, IBPN for short, is concerned with determining the minimum perturbation to the item-size vector so that all the items can be packed into K bins or less. It is known that this problem is NP-hard (Chung, 2012). In this paper, we investigate some special cases of IBPN that can be solved in polynomial time. We propose an optimal algorithm for solving the IBPN instances with two distinct item sizes and the instances with large items.

### Inverse Problem Methodology for Parameter Identification of a Separately Excited DC Motor

• Journal of Electrical Engineering and Technology
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• v.4 no.3
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• pp.365-369
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• 2009
• Identification is considered to be among the main applications of inverse theory and its objective for a given physical system is to use data which is easily observable, to infer some of the geometric parameters which are not directly observable. In this paper, a parameter identification method using inverse problem methodology is proposed. The minimisation of the objective function with respect to the desired vector of design parameters is the most important procedure in solving the inverse problem. The conjugate gradient method is used to determine the unknown parameters, and Tikhonov's regularization method is then used to replace the original ill-posed problem with a well-posed problem. The simulation and experimental results are presented and compared.

### Note on the Inverse Metric Traveling Salesman Problem Against the Minimum Spanning Tree Algorithm

• Chung, Yerim
• Management Science and Financial Engineering
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• v.20 no.1
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• pp.17-19
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• 2014
• In this paper, we consider an interesting variant of the inverse minimum traveling salesman problem. Given an instance (G, w) of the minimum traveling salesman problem defined on a metric space, we fix a specified Hamiltonian cycle $HC_0$. The task is then to adjust the edge cost vector w to w' so that the new cost vector w' satisfies the triangle inequality condition and $HC_0$ can be returned by the minimum spanning tree algorithm in the TSP-instance defined with w'. The objective is to minimize the total deviation between the original and the new cost vectors with respect to the $L_1$-norm. We call this problem the inverse metric traveling salesman problem against the minimum spanning tree algorithm and show that it is closely related to the inverse metric spanning tree problem.

### Designing a Microphone Array for Acoustical Inverse Problems (음향학적 역문제를 위한 마이크로폰의 정렬방법)

• Kim, Youngtea
• The Journal of the Acoustical Society of Korea
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• v.23 no.1E
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• pp.3-9
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• 2004
• An important inverse problem in the field of acoustics is that of reconstructing the strengths of a number of sources given a model of transmission paths from the sources to a number of sensors at which measurements are made. In dealing with this kind of the acoustical inverse problem, strengths of the discretised source distribution can be simply deduced from the measured pressure field data and the inversion of corresponding matrix of frequency response functions. However, deducing :he solution of such problems is not straightforward due to the practical difficulty caused by their inherent ill-conditioned behaviour. Therefore, in order to overcome this difficulty associated with the ill-conditioning, the problem is replaced by a nearby well-conditioned problem whose solution approximates the required solution. In this paper a microphone array are identified for which the inverse problem is optimally conditioned, which can be robust to contaminating errors. This involves sampling both source and field in a manner which results in the discrete pressures and source strengths constituting a discrete Fourier transform pair.

### Optimal shape design of a polymer extrusion die by inverse formulation

• Na, Su-Yeon;Lee, Tai-Yong
• 제어로봇시스템학회:학술대회논문집
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• pp.315-318
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• 1995
• The optimum design problem of a coat-hanger die is solved by the inverse formulation. The flow in the die is analyzed using three-dimensional model. The new model for the manifold geometry is developed for the inverse formulation. The inverse problem for the optimum die geometry is formed as the optimization problem whose objective function is the linear combination of the square sum of pressure gradient deviation at die exit and the penalty function relating to the measure of non-smoothness of solution. From the several iterative solutions of the optimization problem, the optimum solution can be obtained automatically while producing the uniform flow rate distribution at die exit.

### AN ITERATIVE DISTRIBUTED SOURCE METHOD FOR THE DIVERGENCE OF SOURCE CURRENT IN EEG INVERSE PROBLEM

• Choi, Jong-Ho;Lee, Chnag-Ock;Jung, Hyun-Kyo
• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.3
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• pp.191-199
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• 2008
• This paper proposes a new method for the inverse problem of the three-dimensional reconstruction of the electrical activity of the brain from electroencephalography (EEG). Compared to conventional direct methods using additional parameters, the proposed approach solves the EEG inverse problem iteratively without any parameter. We describe the Lagrangian corresponding to the minimization problem and suggest the numerical inverse algorithm. The restriction of influence space and the lead field matrix reduce the computational cost in this approach. The reconstructed divergence of primary current converges to a reasonable distribution for three dimensional sphere head model.