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

• Journal of applied mathematics & informatics
• /
• 제29권1_2호
• /
• pp.119-133
• /
• 2011

This paper proposes an infeasible interior-point algorithm with full-Newton step for linear programming. We introduce a special self-regular proximity to induce the feasibility step and also to measure proximity to the central path. The result of polynomial complexity coincides with the best-known iteration bound for infeasible interior-point methods, namely, O(n log n/${\varepsilon}$).

• Journal of applied mathematics & informatics
• /
• 제30권3_4호
• /
• pp.395-411
• /
• 2012

Several methods with order higher than that of Newton methods which are of order 2 have been reported in literature for solving nonlinear equations. The focus of most of these methods was to economize on/minimize the number of function evaluations per iterations. We have demonstrated here that there are several computational pit-falls, such as the violation of fixed-point theorem, that one could encounter while using these methods. Further it was also shown that the overall computational complexity could be more in these high-order methods than that in the second-order Newton method.

• 대한수학회지
• /
• 제33권4호
• /
• pp.865-878
• /
• 1996

We consider numerical methods for finding a solution to a nonlinear system of algebraic equations $$ (1) f(x) = 0, $$ where the function $f : R^n \to R^n$ is ain $x \in R^n$. In [10], a quasi-Gauss-Newton method is proposed and shown the computational efficiency over SQRT algorithm by numerical experiments. The convergence rate of the method has not been proved theoretically. In this paper, we show theoretically that the iterate $x_k$ obtained from the quasi-Gauss-Newton method for the problem (1) actually converges to a root by Kantorovich-type convergence analysis. We also show the rate of convergence of the method is superlinear.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제3권1호
• /
• pp.71-79
• /
• 1999

We consider multi-step quasi-Newton methods for unconstrained optimization. These methods were introduced by Ford and Moghrabi [1, 2], who showed how interpolating curves could be used to derive a generalization of the Secant Equation (the relation normally employed in the construction of quasi-Newton methods). One of the most successful of these multi-step methods makes use of the current approximation to the Hessian to determine the parameterization of the interpolating curve in the variable-space and, hence, the generalized updating formula. In this paper, we investigate new parameterization techniques to the approximate Hessian, in an attempt to determine a better Hessian approximation at each iteration and, thus, improve the numerical performance of such algorithms.

• 대한정형도수물리치료학회지
• /
• 제17권2호
• /
• pp.33-39
• /
• 2011

Background: The purpose of this study was to verify the most effective spinal stabilization exercise program by comparing the activities of muscles contributing to spinal stabilization during 2 types of exercises using 3-D NEWTON and a Gym-ball. Methods: We divided sixteen healthy students to two groups in D city were recruited and each subjects performed two type of exercise. Exercise 1 was performed 3-D NEWTON spinal stabilization training during 4 weeks (n=8). Exercise 2 was performed special training program that use a Gym-ball during 4 weeks (n=8). Results: The group of 3-D NEWTON applying lumbar stabilization kinetic program was increased 18.8s after training. Conclusions: It was revealed the statically significant difference between 3-D NEWTON and Gym-ball lumbar stabilization exercise groups. Therefore it has been turned out that 3-D NEWTON and Gym-ball lumbar stabilization exercise has an effect on the abdominis and trunk muscle strengthening and balance.

• Journal of applied mathematics & informatics
• /
• 제5권2호
• /
• pp.433-448
• /
• 1998

In this study we use inexact Newton-like methods to find solutions of nonlinear operator equations on Banach spaces with a convergence structure. Our technique involves the introduction of a generalized norm as an operator from a linear space into a par-tially ordered Banach space. In this way the metric properties of the examined problem can be analyzed more precisely. Moreover this approach allows us to derive from the same theorem on the one hand semi-local results of kantorovich-type and on the other hand 2global results based on monotonicity considerations. By imposing very general Lipschitz-like conditions on the operators involved on the other hand by choosing our operators appropriately we can find sharper error bounds on the distances involved than before. Furthermore we show that special cases of our results reduce to the corresponding ones already in the literature. Finally our results are used to solve integral equations that cannot be solved with existing methods.

• 충청수학회지
• /
• 제24권3호
• /
• pp.437-447
• /
• 2011

In this paper we present a new variant of the Euler-Chebyshev method for solving nonlinear equations. Analysis of convergence is given to show that the presented methods are at least fifth-order convergent. Several numerical examples are given to illustrate that newly presented methods can be competitive to other known fifth-order methods and the Newton method in the efficiency and performance.

• 전기학회논문지
• /
• 제66권7호
• /
• pp.1053-1058
• /
• 2017

In this paper, the design of iron loss minimization of 600W was performed by using Quasi-Newton method. Stator shoe, the width of stator teeth and yoke, and the length of d-axis flux path were selected as design parameters, and the output characteristics according to each design variable were considered. The objective function was set to minimize iron loss. Using the Quasi-Newton method, the variables converged to the target value while changing simultaneously and multiple times. As the algorithm advanced optimization, the correlation with the behavior of each variable was compared and analyzed.

• Journal of applied mathematics & informatics
• /
• 제4권1호
• /
• pp.83-108
• /
• 1997

Chebysheff-Halley methods are probably the best known cubically convergent iterative procedures for solving nonlinear equa-tions. These methods however require an evaluation of the second Frechet-derivative at each step which means a number of function eval-uations proportional to the cube of the dimension of the space. To re-duce the computational cost we replace the second Frechet derivative with a fixed bounded bilinear operator. Using the majorant method and Newton-Kantorovich type hypotheses we provide sufficient condi-tions for the convergence of our method to a locally unique solution of a nonlinear equation in Banach space. Our method is shown to be faster than Newton's method under the same computational cost. Finally we apply our results to solve nonlinear integral equations appearing in radiative transfer in connection with the problem of determination of the angular distribution of the radiant-flux emerging from a plane radiation field.