• The Korean Journal of Nuclear Medicine Technology
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• v.15 no.1
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• pp.17-24
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• 2011

Purpose: Presently in the nuclear medicine field, the high-speed image reconstruction algorithm like the OSEM algorithm is widely used as the alternative of the filtered back projection method due to the rapid development and application of the digital computer. There is no to relate and if it applies the optimal parameter be clearly determined. In this research, the quality change of the Jaszczak phantom experiment and brain SPECT patient data according to the iteration times and subset number change try to be been put through and analyzed in 3D OSEM reconstruction method of applying 3D beam modeling. Materials and Methods: Patient data from August, 2010 studied and analyzed against 5 patients implementing the brain SPECT until september, 2010 in the nuclear medicine department of ASAN medical center. The phantom image used the mixed Jaszczak phantom equally and obtained the water and 99mTc (500 MBq) in the dual head gamma camera Symbia T2 of Siemens. When reconstructing each image altogether with patient data and phantom data, we changed iteration number as 1, 4, 8, 12, 24 and 30 times and subset number as 2, 4, 8, 16 and 32 times. We reconstructed in reconstructed each image, the variation coefficient for guessing about noise of images and image contrast, FWHM were produced and compared. Results: In patients and phantom experiment data, a contrast and spatial resolution of an image showed the tendency to increase linearly altogether according to the increment of the iteration times and subset number but the variation coefficient did not show the tendency to be improved according to the increase of two parameters. In the comparison according to the scan time, the image contrast and FWHM showed altogether the result of being linearly improved according to the iteration times and subset number increase in projection per 10, 20 and 30 second image but the variation coefficient did not show the tendency to be improved. Conclusion: The linear relationship of the image contrast improved in 3D OSEM reconstruction method image of applying 3D beam modeling through this experiment like the existing 1D and 2D OSEM reconfiguration method according to the iteration times and subset number increase could be confirmed. However, this is simple phantom experiment and the result of obtaining by the some patients limited range and the various variables can be existed. So for generalizing this based on this results of this experiment, there is the excessiveness and the evaluation about 3D OSEM reconfiguration method should be additionally made through experiments after this.

• Journal of the Korean Chemical Society
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• v.42 no.4
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• pp.398-410
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• 1998

For non-linear solution of the Boltzmann equation, the cumulant moment method has been studied. To apply the method to the normal shock wave problem, we restricted ourselves to the monatomic Maxwell molecular gases. The method is based on the iterative approach developed by Maxwell-Ikenberry-Truesdell (MIT). The original MIT approach employs the equilibrium distribution function for the initial values in beginning the iteration. In the present work, we use the Mott-Smith bimodal distribution function to calculate the initial values and follow the MIT iteration procedure. Calculations have been carried out up to the second iteration for the profiles of density, temperature, stress, heat flux, and shock thickness of strong shocks, including the weak shock thickness of Mach range less than 1.4. The first iteration gives a simple analytic expression for the shock profile, and the weak shock thickness limiting law which is in exact accord with the Navier-Stokes theory. The second iteration shows that the calculated strong shock profiles are consistent with the Monte Carlo values quantitatively.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.3
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• pp.451-458
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• 2012

This paper addresses the problem that policy iteration (PI) for continuous-time (CT) systems requires explorations of the state space which is known as persistency of excitation in adaptive control community, and as a result, proposes a PI scheme explorized by an additional probing signal to solve the addressed problem. The proposed PI method efficiently finds in online fashion the related CT linear quadratic (LQ) optimal control without knowing the system matrix A, and guarantees the stability and convergence to the LQ optimal control, which is proven in this paper in the presence of the probing signal. A design method for the probing signal is also presented to balance the exploration of the state space and the control performance. Finally, several simulation results are provided to verify the effectiveness of the proposed explorized PI method.

• Journal of the Korean Mathematical Society
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• v.40 no.1
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• pp.29-40
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• 2003

Let K be a nonempty closed bounded convex subset of an arbitrary smooth Banach space X and T : KlongrightarrowK be a strictly hemi-contractive operator. Under some conditions we obtain that the Mann iteration method with errors both converges strongly to a unique fixed point of T and is almost T-stable on K. The results presented in this paper generalize the corresponding results in [l]-[7], [20] and others.

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

• Communications for Statistical Applications and Methods
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• v.21 no.6
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• pp.513-520
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• 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
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• 1996.11a
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• pp.301-305
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• 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.

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

• Journal of Internet Computing and Services
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• v.4 no.5
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• pp.51-60
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• 2003

Asynchronous iteration is a way to reduce performance degradation of some parallel algorithms due to load imbalance or transmission delay between computing nodes, which requires asymmetric communication between the nodes of different speeds. To implement such asynchronous communication on distributed memory systems, we suggest an MPMD method that creates an additional separate server process on each computing node, and compare it with an SPMD method that creates a single process per node.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.205-229
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• 2022

The aim of this paper is to obtain some results which belong to fixed point theory such as strong convergence, rate of convergence, stability, and data dependence by using the new Jungck-type iteration method for a mapping defined in complex-valued Banach spaces. In addition, some of these results are supported by nontrivial numerical examples. Finally, it is shown that the sequence obtained from the new iteration method converges to the solution of the functional integral equation in complex-valued Banach spaces. The results obtained in this paper may be interpreted as a generalization and improvement of the previously known results.