• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.14 no.2
• /
• pp.113-124
• /
• 2010

We consider matrix polynomial which has the form $P_1(X)=A_oX^m+A_1X^{m-1}+...+A_m=0$ where X and $A_i$ are $n{\times}n$ matrices with real elements. In this paper, we propose an iterative method for the symmetric and generalized centro-symmetric solution to the Newton step for solving the equation $P_1(X)$. Then we show that a symmetric and generalized centro-symmetric solvent of the matrix polynomial can be obtained by our Newton's method. Finally, we give some numerical experiments that confirm the theoretical results.

• Journal of the Korean Mathematical Society
• /
• v.52 no.2
• /
• pp.349-372
• /
• 2015

This paper concerns with exploiting an oblique projection technique to solve a general class of large and sparse least squares problem over symmetric arrowhead matrices. As a matter of fact, we develop the conjugate gradient least squares (CGLS) algorithm to obtain the minimum norm symmetric arrowhead least squares solution of the general coupled matrix equations. Furthermore, an approach is offered for computing the optimal approximate symmetric arrowhead solution of the mentioned least squares problem corresponding to a given arbitrary matrix group. In addition, the minimization property of the proposed algorithm is established by utilizing the feature of approximate solutions derived by the projection method. Finally, some numerical experiments are examined which reveal the applicability and feasibility of the handled algorithm.

• Journal of applied mathematics & informatics
• /
• v.28 no.1_2
• /
• pp.465-472
• /
• 2010

The purpose of this article is to introduce a new generalized class of the Wiener-Hopf equations and a new generalized class of the variational inequalities. Using the projection technique, we show that the generalized Wiener-Hopf equations are equivalent to the generalized variational inequalities. We use this alternative equivalence to suggest and analyze an iterative scheme for finding the solution of the generalized Wiener-Hopf equations and the solution of the generalized variational inequalities. The results presented in this paper may be viewed as significant and improvement of the previously known results. In special, our results improve and extend the resent results of M.A. Noor and Z.Y.Huang[M.A. Noor and Z.Y.Huang, Wiener-Hopf equation technique for variational inequalities and nonexpansive mappings, Appl. Math. Comput.(2007), doi:10.1016/j.amc.2007.02.117].

• Proceedings of the KIEE Conference
• /
• 1997.11a
• /
• pp.231-234
• /
• 1997

This paper presents improved direct method for calculating the closest saddle node bifurcation (CSNB) point, which is also applicable to the selection of appropriate load shedding, reactive power compensation point detection. The proposed method reduced dimension of nonlinear equation compared with that of Dobson's direct method. The improved direct method, utilizing Newton Iterative method converges very quickly. But it diverges if the initial guess is not very close to CSNB. So the direct method is performed with the initial values obtained by carrying out the iterative method twice, which is considered most efficient at this time. Since sparsity techniques can be employed, this method is a good choice to a large scale system on-line application. Proposed method has been tested for 5-bus, New England 30-bus system.

• Proceedings of the KSME Conference
• /
• 2000.11a
• /
• pp.671-675
• /
• 2000

In this study, an FRF-based structural damage identification method (SDIM) is proposed for plate structures. The present SDIM is derived from the partial differential equation of motion of the damaged plate, in which damage is characterized by damage distribution function. Various factors that might affect the accuracy of the damage identification are investigated. They include the number of modal data used in the analysis and the damage-induced modal coupling. In the present SDIM, an efficient iterative damage self-search method is introduced. The iterative damage search method efficiently reduces the size of problem by searching out and then by removing all damage-free zones at each iteration of damage identification analysis. The feasibility of the present SDIM is studied by some numerically simulated tests.

• Journal of the Korean Society of Industry Convergence
• /
• v.22 no.4
• /
• pp.415-425
• /
• 2019

This study proposes a new approach to control Moving Stuff Action Through Iterative Learning robot with dual arm for smart factory. When robot moves object with dual arm, not only position of each hand but also contact force at surface of an object should be considered. However, it is not easy to determine every parameters for planning trajectory of the an object and grasping object concerning about variety compliant environment. On the other hand, human knows how to move an object gracefully by using eyes and feel of hands which means that robot could learn position and force from human demonstration so that robot can use learned task at variety case. This paper suggest a way how to learn dynamic equation which concern about both of position and path.

• Journal of the Korean Mathematical Society
• /
• v.59 no.6
• /
• pp.1067-1082
• /
• 2022

This paper presents a new optimal three-step eighth-order family of iterative methods for finding multiple roots of nonlinear equations. Different from the all existing optimal methods of the eighth-order, the new iterative scheme is constructed using one function and three derivative evaluations per iteration, preserving the efficiency and optimality in the sense of Kung-Traub's conjecture. Theoretical results are verified through several standard numerical test examples. The basins of attraction for several polynomials are also given to illustrate the dynamical behaviour and the obtained results show better stability compared to the recently developed optimal methods.

• Kyungpook Mathematical Journal
• /
• v.62 no.4
• /
• pp.699-713
• /
• 2022

This paper proposes a hybrid successive over-relaxation iterative method for the numerical solution of a nonlinear diffusion in a one-dimensional porous medium. The considered mathematical model is discretized using a computational complexity reduction scheme called half-sweep finite differences. The local truncation error and the analysis of the stability of the scheme are discussed. The proposed iterative method, which uses explicit group technique and modified successive over-relaxation, is formulated systematically. This method improves the efficiency of obtaining the solution in terms of total iterations and program elapsed time. The accuracy of the proposed method, which is measured using the magnitude of absolute errors, is promising. Numerical convergence tests of the proposed method are also provided. Some numerical experiments are delivered using initial-boundary value problems to show the superiority of the proposed method against some existing numerical methods.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.25 no.5
• /
• pp.601-606
• /
• 2014

The IPO(Iterative Physical Optics) method repeatedly applies the well-known PO(Physical Optics) approximation to calculate the scattered field by a large object. Thus, the IPO method can consider the multiple scattering in the object, which is ignored for the PO approximation. This kind of iteration can improve the final accuracy of the induced current on the scatterer, which can result in the enhancement of the accuracy of the RCS(Radar Cross Section) of the scatterer. Since the IPO method can not exactly but approximately solve the required integral equation, however, the convergence of the IPO solution can not be guaranteed. Hence, we apply the famous techniques used in the inversion of a matrix to the IPO method, which include Jacobi, Gauss-Seidel, SOR(Successive Over Relaxation) and Richardson methods. The proposed IPO methods can efficiently calculate the RCS of a large scatterer, and are numerically verified.

• Journal of applied mathematics & informatics
• /
• v.7 no.2
• /
• pp.605-615
• /
• 2000

Let E be a real Banach space with property (U,${\lambda}$,m+1,m);${\lambda}{\ge}$0; m${\in}N$, and let C be a nonempty closed convex and bounded subset of E. Suppose T: $C{\leftrightarro}C$ is a strongly accretive map, It is proved that each of the two well known fixed point iteration methods( the Mann and Ishikawa iteration methods.), under suitable conditions , converges strongly to a solution of the equation Tx=f.