• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.345-360
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• 2001

Affine invariant sufficient conditions are given for two local convergence theorems involving inexact Newton-like methods. The first uses conditions on the first Frechet-derivative whereas the second theorem employs hypotheses on the mth(m≥2 an integer). Radius of convergence as well as rate of convergence results are derived. Results involving superlinear convergence and known to be true for inexact Newton methods are extended here. Moreover, we show that under hypotheses on the mth Frechet-derivative our radius of convergence can sometimes be larger than the corresponding one in [10]. This allows a wider choice for the initial guess. A numerical example is also provided to show that our radius of convergence is larger than the one in [10].

• 한국해양공학회:학술대회논문집
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• 한국해양공학회 2002년도 춘계학술대회 논문집
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• pp.231-236
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• 2002

By using the infinite dimensional optimization[Jang and Kinoshita(2000)]. which is based on the Hilbert space theory, optimal marine propellers are studied. The mathematical uniqueness for the optimized propeller is shown in this study. As a numerical example, the MAU type propeller is considered and used as the initial guess for the optimization method. The numerical results for an optimal marine propeller is illustrated for the pitch distribution.

• Journal of applied mathematics & informatics
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• 제6권2호
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• pp.369-378
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• 1999

In This study we examine the applicability of Newton's method and the modified Newton's method for a, pp.oximating a lo-cally unique solution of a nonlinear equation in a Banach space. We assume that the newton-Kantorovich hypothesis for Newton's method is violated but the corresponding condition for the modified Newton method holds. Under these conditions there is no guaran-tee that Newton's method starting from the same initial guess as the modified Newton's method converges. Hence it seems that we must always use the modified Newton method under these condi-tions. However we provide a numerical example to demonstrate that in practice this may not be a good decision.

• Journal of applied mathematics & informatics
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• 제6권2호
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• pp.393-406
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• 1999

Affine invariant sufficient conditions are given for two local convergence theorems involving inexact Newton-like methods. The first uses conditions on the first Frechet-derivative whereas the second theorem employs hypotheses on the second. Radius of con-vergence as well as rate of convergence results are derived. Results involving superlinear convergence and known to be true for inexact Newton methods are extended here. Moreover we show that under hypotheses on the second Frechet-derivation our radius of convergence results are derived. Results involving superlinear convergence and known to be true or inexact Newton methods are extended here. Moreover we show that under hypotheses on the second Frechet-derivative our radius of conver-gence is larger than the corresponding one in [10]. This allows a wider choice for the initial guess. A numerical example is also pro-vided to show that our radius of convergence is larger then the one in [10].

• 한국정밀공학회지
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• 제16권2호통권95호
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• pp.164-175
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• 1999

If the camera plane is nearly parallel to the calibration board on which objects are defined, most of existing calibration approaches such as Tsai's radial-alignment-constraint method cannot be applied. Recently, for such an ill-conditioned case, Zhuang & Wu suggested the linear two-stage calibration algorithm assuming that the exact values of focal length and scale factor are known a priori. In this paper, we developed an iterative two-stage algorithm starts with initial guess fo the two parameters to determine the value of the others using Zhuang & Wu's method. In the second stage, the two parameters are locally optimized. This process is repeated until any improvement cannot be expected any more. The performance comparison between Zhuang & Wu's method and our algorithm shows the superiority of ours. Also included are the computational results for the effects of the distribution and the number of calibration points on the calibration performance.

• 대한수학회보
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• 제48권5호
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• pp.1079-1092
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• 2011

We consider the Newton's method for an direct solver of the optimal control problems of the Navier-Stokes equations. We show that the finite element solutions of the optimal control problem for Stoke equations may be chosen as the initial guess for the quadratic convergence of Newton's algorithm applied to the optimal control problem for the Navier-Stokes equations provided there are sufficiently small mesh size h and the moderate Reynold's number.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 한국자동제어학술회의논문집(국내학술편); 포항공과대학교, 포항; 24-26 Oct. 1996
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• pp.988-991
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• 1996

The purpose of this thesis is to develop methods of designing robust LQR/LQG controllers for time-varying systems with real parametric uncertainties. Controller design that meet desired performance and robust specifications is one of the most important unsolved problems in control engineering. We propose a new framework to solve these problems using Linear Matrix Inequalities (LMls) which have gained much attention in recent years, for their computational tractability and usefulness in control engineering. In Robust LQR case, the formulation of LMI based problem is straightforward and we can say that the obtained solution is the global optimum because the transformed problem is convex. In Robust LQG case, the formulation is difficult because the objective function and constraint are all nonlinear, therefore these are not treatable directly by LMI. We propose a sequential solving method which consist of a block-diagonal approach and a full-block approach. Block-diagonal approach gives a conservative solution and it is used as a initial guess for a full-block approach. In full-block approach two LMIs are solved sequentially in iterative manner. Because this algorithm must be solved iteratively, the obtained solution may not be globally optimal.

• 한국정밀공학회지
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• 제13권9호
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• pp.84-93
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• 1996

This paper describes the development of new feature positioning method which embedded into the top-down assembly modeling system supporting conceptual design. In this work, the user provides the geometric constraints representing the position and size of features, then the system calculates their proper solution. The use of geometric constraints which are easy to understand intuitively enables the user to represent his design intents about geometric shapes, and enables the system to propagate the changes automatically when some editing occurs. To find the proper solution of given constraints, the Selective Solving Method in which the redundant or conflict equations are detected and discarded is devised. The validity of feature shapes satisfying the constraints can be maintained by this technique, and under or over constrained user-defined constraints can also be estimated. The problems such as getting the initial guess, controlling the multiple solutions, and dealing with objects of rotational symmetry are also resolved. Through this work, the feature based modeling system can support more general and convenient modeling method, and keeps the model being valid during modifying models.

• 제어로봇시스템학회논문지
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• 제13권7호
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• pp.683-687
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• 2007

In last decades, several linearization methods for the AOA measurements have been proposed, for example, Gauss-Newton method and Closed-Form solution. Gauss-Newton method can achieve high accuracy, but the convergence of the iterative process is not always ensured if the initial guess is not accurate enough. Closed-Form solution provides a non-iterative solution and it is less computational. It does not suffer from convergence problem, but estimation error is somewhat larger. This paper proposes a Self-Tuning Weighted Least Square AOA algorithm that is a modified version of the conventional Closed-Form solution. In order to estimate the error covariance matrix as a weight, a two-step estimation technique is used. Simulation results show that the proposed method has smaller positioning error compared to the existing methods.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 2006년도 제5회 박판성형 SYMPOSIUM
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• pp.68-71
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• 2006

Traditional section-based method develops blank along section planes and find trimming line by generating loop of end points. This method suffers from inaccurate results for regions with out-of-section motion. In this study, new fast method to find feasible trimming line is proposed. One step FEM is used to analyze the flanging and incremental development method is proposed to handle bad-shaped mesh and undercut part. Also in order to remedy mesh distortion during development, energy minimization technique is utilized. The proposed method is verified by shrink/stretch flange forming and successfully applied to the complex industrial applications such as door outer flanging process.