• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2009.01a
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• pp.103-107
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• 2009

This paper presents how to minimize the second-order cone programming problem occurring in the 3D reconstruction of multiple views. The $L_{\infty}$-norm minimization is done by a series of the minimization of the maximum infeasibility. Since the problem has many inequality constraints, we have to adopt methods of the interior point algorithm, in which the inequalities are sequentially approximated by log-barrier functions. An initial feasible solution is found easily by the construction of the problem. Actual computing is done by an iterative Newton-style update. When we apply the interior point method to the problem of reconstructing the structure and motion, every Newton update requires to solve a very large system of linear equations. We show that the sparse bundle-adjustment technique can be utilized in the same way during the Newton update, and therefore we obtain a very efficient computation.

• Proceedings of the KIEE Conference
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• 1998.11a
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• pp.259-262
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• 1998

This paper presents a new eigenvalue calculation methods in AESOPS algorithm. The source program of the AESOPS algorithm is modified to practice in PC environment. Window95 is used as an operating system of PC and MicroSoft Power Station is used to compile the fortran source program. The heuristically approximated eigenvalue calculation method of the AESOPS algorithm is transformed to the Newton Raphson Method which is largely used in the nonlinear numerical analysis. The new methods are developed from the AESOPS algorithm and thus only a few calculation steps are added to practice the proposed algorithm.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.5
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• pp.375-380
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• 2007

The nonlinear aerodynamic analysis of wing with control surface is performed using the frequency-domain panel method. To take into consideration the nonlinear aerodynamic characteristics of wing an iterative decambering approach is introduced. The iterative decambering approach uses the known aerodynamic characteristics of airfoil to calculate the aerodynamic characteristics of wing. The multi-dimensional Newton iteration is used to account for the coupling between the different sections of wing. The present method is verified by showing that it produces results that are in good agreement with experiments. The present method will be useful for the analysis of aircraft in the conceptual design because the present method can calculate promptly the nonlinear aerodynamic characteristics of wing with a few computing resources.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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• pp.79-92
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• 2000

We investigate numerical properties of Newton's algorithm for improving an eigenpair of a real matrix A using only fixed precision arithmetic. We show that under natural assumptions it produces an eigenpair of a componentwise small relative perturbation of the data matrix A.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.295-302
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• 2021

In this paper, we propose a new iterative algorithm to automatically prove the existence of solutions for a unilateral boundary value problems for second order equations.

• Structural Engineering and Mechanics
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• v.36 no.5
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• pp.529-544
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• 2010

Nonlinear equations of structures are generally solved numerically by the iterative solution of linear equations. However, this iterative procedure diverges when the tangent stiffness is ill-conditioned which occurs near limit points. In other words, a major challenge with simple iterative methods is failure caused by a singular or near singular Jacobian matrix. In this paper, using the Newton-Raphson algorithm based on Davidenko's equations, the iterations can traverse the limit point without difficulty. It is argued that the propose algorithm may be both more computationally efficient and more robust compared to the other algorithm when tracing path through severe nonlinearities such as those associated with structural collapse. Two frames are analyzed using the proposed algorithm and the results are compared with the previous methods. The ability of the proposed method, particularly for tracing the limit points, is demonstrated by those numerical examples.

• Journal of IKEEE
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• v.19 no.1
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• pp.33-40
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• 2015

Inverse problem in electrical impedance tomography (EIT) is highly ill-posed therefore prior information is used to mitigate the ill-posedness. Regularization methods are often adopted in solving EIT inverse problem to have satisfactory reconstruction performance. In solving the EIT inverse problem, iterative Gauss-Newton method is generally used due to its accuracy and fast convergence. However, its performance is still suboptimal and mainly depends on the selection of regularization parameter. Although, there are few methods available to determine the regularization parameter such as L-curve method they are sometimes not applicable for all cases. Moreover, regularization parameter is a scalar and it is fixed during iteration process. Therefore, in this paper, a novel method is used to determine the regularization parameter to improve reconstruction performance. Conductivity norm is calculated at each iteration step and it used to obtain the regularization parameter which is a diagonal matrix in this case. The proposed method is applied to human thorax imaging and the reconstruction performance is compared with traditional methods. From numerical results, improved performance of proposed method is seen as compared to conventional methods.

• Journal of the Korean Society of Propulsion Engineers
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• v.5 no.1
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• pp.69-75
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• 2001

Linear GPA(Gas Path Analysis) and non-linear GPA programs for performance diagnostics of a turboprop engine were developed, and a study for selection of optimal measurement variables was performed. Simultaneous faults in the compressor, the compressor turbine and the power turbine, which occur damage of the engine, were assumed. The non-linear GPA analysis was carried out with an iterative method, where the performance degradation rate of independent parameters was divided into same intervals. It was compared with the result by the Newton-Raphson method for observing the effect of an iterative method. According to the analysis result, it was found that performance of non-linear GPA can be influenced on the type of the iterative method. For showing effects of the number of measurement variables both the linear and non-linear GPAs were analyzed with 10, 8 and 6 measurement sets, respectively. RMS error between them were compared each other. It was realized that the more measurement parameters are used, and the more accurate result may be obtained. However much better result can be obtained with measurement parameters selected properly Moreover, RMS error by using non-linear GPA was less than that by using linear GPA.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.677-693
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• 2018

In this work, we generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study its local convergence to approximate a locally-unique solution of a system of nonlinear equations. The convergence in this study is shown under hypotheses only on the first derivative. Our analysis avoids the usual Taylor expansions requiring higher order derivatives but uses generalized Lipschitz-type conditions only on the first derivative. Moreover, our new approach provides computable radius of convergence as well as error bounds on the distances involved and estimates on the uniqueness of the solution based on some functions appearing in these generalized conditions. Such estimates are not provided in the approaches using Taylor expansions of higher order derivatives which may not exist or may be very expensive or impossible to compute. The convergence order is computed using computational order of convergence or approximate computational order of convergence which do not require usage of higher derivatives. This technique can be applied to any iterative method using Taylor expansions involving high order derivatives. The study of the local convergence based on Lipschitz constants is important because it provides the degree of difficulty for choosing initial points. In this sense the applicability of the method is expanded. Finally, numerical examples are provided to verify the theoretical results and to show the convergence behavior.

• Journal of Korean Association for Spatial Structures
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• v.3 no.4 s.10
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• pp.85-92
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• 2003

In this work, a finite element model is presented for geometrically non-linear analysis of shell structures. Finite element by using a three-node flat triangular shell element is formulated. The non-linear incremental equilibrium equations are formulated by using an updated Lagrangian formulation and the solutions are obtained with the incremental/iterative Newton-Raphson method and arc length method. Some of results are presented for shell structures. The obtained results are in good agreement with the results available in existing literature.