• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.23 no.4
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• pp.337-344
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• 2014

While implicit integration methods such as Newton's method have excellent stability for the analysis of stiff and constrained mechanical systems, they have the drawback that the evaluation and LU-factorization of the system Jacobian matrix required at every time step are time-consuming. This paper proposes a Jacobian update-free Newton's method in order to overcome these defects. Because the motions of all bodies in a vehicle model are limited with respect to the chassis body, the equations are formulated with respect to the moving chassis-body reference frame instead of the fixed inertial reference frame. This makes the system Jacobian remain nearly constant, and thus allows the Newton's method to be free from the Jacobian update. Consequently, the proposed method significantly decreases the computational cost of the vehicle dynamic simulation. This paper provides detailed generalized formulation procedures for the equations of motion, constraint equations, and generalized forces of the proposed method.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.19 no.3
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• pp.119-126
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• 2005

Electrical resistance tomography(ERT) maps resistivity values of the soil subsurface and characterizes buried objects. The characterization includes location, size and resistivity of buried objects. In this paper, Gauss-Newton, truncated least squares(TLS) and simultaneous iterative reconstruction technique(SIRT) methods are presented for the solution of the ERT image reconstruction. Computer simulations show that the spatial resolution of the reconstructed images by the TLS approach is improved as compared to those obtained by the Gauss-Newton and SIRT method.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.314-317
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• 1993

In this paper, the IPE(Iterative Parameter Estimation) methods for the nonlinear measurements are proposed. The IPE methods convert the problems of the parameter estimation for the nonlinear measurements to that of the solution of the nonlinear equations approximately and use several iterative numerical solutions, such as fixed points theory, Newton's methods, quasi-Newton's methods and steepest descent techniques. the IPE methods for the nonlinear measurements-in the case of the error estimation for the inertial navigation systems are simulated, and it is found that the estimation errors for the nonlinear measurements decrease rapidly and converge to almost that of the linear LSE(Least Squares Estimation) when the IPE methods are applied.

• Computational Structural Engineering
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• v.11 no.1
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• pp.205-216
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• 1998

A solution method is presented to solve the eigenvalue problem arising in the dynamic analysis of nonclassicary damped structural systems with multiple eigenvalues. The proposed method is obtained by applying the modified Newton-Raphson technique and the orthonormal condition of the eigenvectors to the linear eigenproblem through matrix augmentation of the quadratic eigenvalue problem. In the iteration methods such as the inverse iteration method and the subspace iteration method, singularity may be occurred during the factorizing process when the shift value is close to an eigenvalue of the system. However, even though the shift value is an eigenvalue of the system, the proposed method provides nonsingularity, and that is analytically proved. Since the modified Newton-Raphson technique is adopted to the proposed method, initial values are need. Because the Lanczos method effectively produces better initial values than other methods, the results of the Lanczos method are taken as the initial values of the proposed method. Two numerical examples are presented to demonstrate the effectiveness of the proposed method and the results are compared with those of the well-known subspace iteration method and the Lanczos method.

• 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 applied mathematics & informatics
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• v.33 no.1_2
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• pp.61-76
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• 2015

In this paper, a fifth order extension of Potra's third order iterative method is proposed for solving nonlinear equations. A convergence theorem along with the error bounds is established. The method takes three functions and one derivative evaluations giving its efficiency index equals to 1.495. Some numerical examples are also solved and the results obtained are compared with some other existing fifth order methods. Next, the interval extension of both third and fifth order Potra's method are developed by using the concepts of interval analysis. Convergence analysis of these methods are discussed to establish their third and fifth orders respectively. A number of numerical examples are worked out using INTLAB in order to demonstrate the efficacy of the methods. The results of the proposed methods are compared with the results of the interval Newton method.

• Journal of information and communication convergence engineering
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• v.10 no.1
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• pp.66-70
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• 2012

Conformal mapping has been a familiar tool of science and engineering for generations. Determination of a conformal map from the unit disk onto the Jordan region is reduced to solving the Theodorsen equation, which is an integral equation for boundary correspondence functions. There are many methods for solving the Theodorsen equation. It is the goal of numerical conformal mapping to find methods that are at once fast, accurate, and reliable. In this paper, we analyze Niethammer’s solution based on successive over-relaxation (SOR) iteration and Wegmann’s solution based on Newton iteration, and compare them to determine which one is more effective. Through several numerical experiments with these two methods, we can see that Niethammer’s method is more effective than Wegmann’s when the degree of the problem is low and Wegmann’s method is more effective than Niethammer’s when the degree of the problem is high.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.10
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• pp.962-967
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• 2006

Indoor positioning is highlighted recently, and various kinds of indoor positioning systems are under developments. Since positioning systems have their own characteristics, proper positioning scheme should be chosen according to the required specifications. Positioning methods are classified into time-based and angle-based one. This paper presents the error analysis of time-based and angle-based location methods. Because measurements of these methods are nonlinear, linearizations are needed in both cases to estimate the user position. In the linearization, Gauss-Newton method is used in both cases. To analyze the position error, we investigate the error ellipse parameters that include eccentricity, rotation angle, and the size of ellipse. Simulation results show that the major axes of TOA and AOA method lie in different quadrants at most region of workspace, especially where the geometry is poor. When the TOA/AOA hybrid is employed, it is found that the error ellipse is reduced to the intersection of ellipses of TOA and AOA.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.6
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• pp.751-759
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• 2007

We have developed several methods for the optimization problem having large-scale and highly nonlinear system. First, step by step method in optimization process was employed to improve the convergence. In addition, techniques of furnishing good initial guesses for analysis using sensitivity information acquired from optimization iteration, and of manipulating analysis/optimization convergency criterion motivated from simultaneous technique were used. We applied them to flow control problem and verified their efficiency and robustness. However, they are based on quasi-Newton method that approximate the Hessian matrix using exact first derivatives. However solution of the Navier-Stokes equations are very cost, so we want to improve the efficiency of the optimization algorithm as much as possible. Thus we develop a true Newton method that uses exact Hessian matrix. And we apply that to the three-dimensional problem of flow around a sphere. This problem is certainly intractable with existing methods for optimal flow control. However, we can attack such problems with the methods that we developed previously and true Newton method.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.557-562
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• 1991

In this paper, we present new methods for solving the inverse kinematics associated with 6 degree of freedoms manipulator by the numerical method. This method will be based on tracking stability of special nonlinear dynamical systems, and differs from the typical techniques based by the Newton-Gauss or Newton-Raphson method for solving nonlinear equations. This simulation results show that the new method is solving the inverse kinematics of PUMA 560 without the derivative of a given task space trajectories.