• Bulletin of the Korean Mathematical Society
• /
• v.47 no.5
• /
• pp.973-985
• /
• 2010

We introduce an iteration scheme for approximating common fixed points of two mappings. On one hand, it extends a scheme due to Agarwal et al. [2] to the case of two mappings while on the other hand, it is faster than both the Ishikawa type scheme and the one studied by Yao and Chen [18] for the purpose in some sense. Using this scheme, we prove some weak and strong convergence results for approximating common fixed points of two nonexpansive self mappings. We also outline the proofs of these results to the case of nonexpansive nonself mappings.

• Journal of the Korean Mathematical Society
• /
• v.55 no.6
• /
• pp.1529-1540
• /
• 2018

The matrix equation $X^p+A^*XA=Q$ has been studied to find the positive definite solution in several researches. In this paper, we consider fixed-point iteration and Newton's method for finding the matrix p-th root. From these two considerations, we will use the Newton-Schulz algorithm (N.S.A). We will show the residual relation and the local convergence of the fixed-point iteration. The local convergence guarantees the convergence of N.S.A. We also show numerical experiments and easily check that the N.S. algorithm reduce the CPU-time significantly.

• The KIPS Transactions:PartA
• /
• v.12A no.5 s.95
• /
• pp.421-426
• /
• 2005

In a large scale parallel computation, some processor or communication link failure results in a waste of huge amount of CPU hours. However, MPI in its current specification gives the user no possibility to handle such a problem. In this paper, we propose an application-level fault tolerant linear system solver by using an MPMD-type asynchronous iteration, purely on the basis of the MPI standard without using any non-standard fault-tolerant MPI library.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.13 no.5
• /
• pp.437-443
• /
• 1988

We calculate the distribution of the current on the strip by the incident waves on the infinite conducting strip line. The boundary equations represented as the spatial domain function become very complicated equations including convolution integral. Transformed it to the spectral domain, we have a very simple equation is composed by some algebraic multiplication of the current density function and Green's function. the acceleration of iteration procedure is achieved by Kastner's method. The result of iteration gives us the optimum value when it satisfies the iteration stop condition presented in this paper. We confirmed that the induced current density distribution on the stripline has been changed as variaties of the width.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.35 no.9C
• /
• pp.743-747
• /
• 2010

This paper presents an iterative adaptive hybrid image restoration algorithm for fast convergence. The local variance, mean, and maximum value are used to constrain the solution space. These parameters are computed at each iteration step using partially restored image at each iteration, and they are used to impose the degree of local smoothness on the solution. The resulting iterative algorithm exhibits increased convergence speed and better performance than typical regularized constrained least squares (RCLS) approach.

• Korean Journal of Mathematics
• /
• v.16 no.4
• /
• pp.481-494
• /
• 2008

Iteration functions $K_m(z)$ and $U_m(z)$, $m{\geq}2$are defined recursively using the determinant of a matrix. We show that the fixed-iterations of $K_m(z)$ and $U_m(z)$ converge to a simple zero with order of convergence m and give closed form expansions of $K_m(z)$ and $U_m(z)$: To show the convergence, we derive a recursion formula for $L_m$ and then apply the idea of Ford or Pomentale. We also find a Toeplitz matrix whose determinant is $L_m(z)/(f^{\prime})^m$, and then we adapt the well-known results of Gerlach and Kalantari et.al. to give closed form expansions.

• Communications for Statistical Applications and Methods
• /
• v.21 no.6
• /
• pp.513-520
• /
• 2014

We study numerical methods to obtain the stationary probabilities of continuous-time Markov chains whose embedded chains are periodic. The power method is applied to the balance equations of the periodic embedded Markov chains. The power method can have the convergence speed of exponential rate that is ambiguous in its application to original continuous-time Markov chains since the embedded chains are discrete-time processes. An illustrative example is presented to investigate the numerical iteration of this paper. A numerical study shows that a rapid and stable solution for stationary probabilities can be achieved regardless of periodicity and initial conditions.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 1996.11a
• /
• pp.301-305
• /
• 1996

$\mu$ theory can handle the parametric uncertainty and produces more non-conservative controller than H$_{\infty}$ control theory. However an existing solution of the theory, D-K iteration, creates a controller of huge order and cannot handle the real or mixed real-complex perturbation sets. In this paper, we use genetic algorithms to solve these problems of the D-K iteration method. The Youla parameterization is used to obtain all stabilizing controllers and the genetic algorithms determines the values of the state feedback gain, the observer gain, and Q parameter to minimize $\mu$, the structured singular value, of given system. From an example, we show that this method produces lower order controller which controls a real parameter-perturbed plant than D-K iteration method.

• KIEE International Transactions on Electrophysics and Applications
• /
• v.3C no.5
• /
• pp.199-206
• /
• 2003

Numerical solutions to complex characteristic equations are quite often required to solve electromagnetic wave problems. In general, two traditional complex root search algorithms, the Newton-Raphson method and the Muller method, are used to produce such solutions. However, when utilizing these two methods, the choice of the initial iteration value is very sensitive, otherwise, the iteration can fail to converge into a solution. Thus, as an alternative approach, where the selection of the initial iteration value is more relaxed and the computation speed is high, Davidenko's method is used to determine accurate complex propagation constants for leaky circular symmetric modes in circular dielectric rod waveguides. Based on a precise determination of the complex propagation constants, the leaky mode characteristics of several lower-order circular symmetric modes are then numerically analyzed. In addition, no modification of the characteristic equation is required for the application of Davidenko's method.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2001.10a
• /
• pp.83-90
• /
• 2001

In the design of cable structures it is necessary to know the initial shape of the cable. The geometrical condition and the equilibrium equation of the cable are needed. Because the equilibrium equation is expressed by the simultaneous equations of second order, it is almost impossible to solve with elimination method. To solve it, we must use iteration method. In this study, the algorithm which can reduce the number of iteration and calculate shape of the cable is developed and compared with measured data through the laboratory test and the results represent good agreements.