• Journal of the Korean Statistical Society
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• v.31 no.1
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• pp.33-43
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• 2002

The empirical Bayes linear loss two-action problem is studied. An empirical Bayes test $\delta$$_{n}$ $^{*}$ is proposed. It is shown that $\delta$$_{n}$ $^{*}$ is asymptotically optimal in the sense that its regret converges to zero at a rate $n^{-1}$ over a class of priors and the rate $n^{-1}$ is the optimal rate of convergence of empirical Bayes tests.sts.

• 전기의세계
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• v.17 no.1
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• pp.48-50
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• 1968

The convergence rate of Bayes' learning process is investigated for a binomial random variable. A measure of the rate of convergence is proposed and it is found that such a measure can be approximated by an exponential function of the number of observations.

• Tunnel and Underground Space
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• v.23 no.2
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• pp.110-119
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• 2013

It is generalized to measure the arch settlement and convergence during tunnel construction for monitoring its mechanical stability. The initial convergence rate a day is defined from the first convergence measurement and the final convergence defined as the convergence measured lastly. The initial and the final tunnel arch settlement are defined like the preceding convergence. In the study, the relations between the initial and final displacements of a shallow tunnel are analyzed. The measurements were performed in the tunnel of subway 906 construction site in Seoul. The overburden is 10-20 m and the tunnel goes through weathered soil/rock. The width and height of the tunnel are about 11.5 m, 10m, respectively. So this is a shallow tunnel in weak rock. The length of tunnel is about 1,820 m and the tunnel was constructed in 2 stages, dividing upper and lower half. The numbers of measurement locations of arch settlement and convergence are 184 and 258, respectively. As a result, the initial displacement rate and the final displacement are comparatively larger in the section of weathered soil.

• Journal of Korean Society for Quality Management
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• v.30 no.4
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• pp.68-77
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• 2002

EM algorithm has good convergence rate for numerical procedures which converges on very small step. In the case of proportion estimation in a mixed distribution which has very big incomplete data or of update of new data continuously, however, EM algorithm highly depends on a initial value with slow convergence ratio. There have been many studies to improve the convergence rate of EM algorithm in estimating the proportion parameter of a mixed data. Among them, dynamic EM algorithm by Hurray Jorgensen and Titterington algorithm by D. M. Titterington are proven to have better convergence rate than the standard EM algorithm, when a new data is continuously updated. In this paper we suggest dynamic EM algorithm and Titterington algorithm for the estimation of a mixed Poisson distribution and compare them in terms of convergence rate by using a simulation method.

• Journal of information and communication convergence engineering
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• v.2 no.3
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• pp.177-181
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• 2004

In this paper, we suggest an Iris recognition system with an excellent recognition rate and confidence as an alternative biometric recognition technique that solves the limit in an existing individual discrimination. For its implementation, we extracted coefficients feature values with the wavelet transformation mainly used in the signal processing, and we used neural network to see a recognition rate. However, Scale Conjugate Gradient of nonlinear optimum method mainly used in neural network is not suitable to solve the optimum problem for its slow velocity of convergence. So we intended to enhance the recognition rate by using Levenberg-Marquardt Back-propagation which supplements existing Scale Conjugate Gradient for an implementation of the iris recognition system. We improved convergence velocity, efficiency, and stability by changing properly the size according to both convergence rate of solution and variation rate of variable vector with the implementation of an applied algorithm.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.671-681
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• 2014

In this paper, we consider general Beta operators, which is a general sequence of integral type operators including Beta function. We study the King type Beta operators which preserves the third test function $x^2$. We obtain some approximation properties, which include rate of convergence and statistical convergence. Finally, we show how to reach best estimation by these operators.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.865-878
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• 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 applied mathematics & informatics
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• v.14 no.1_2
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• pp.329-341
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• 2004

We consider the rate of convergence for a class of perturbed hemivariational inequalities in reflexive Banach Spaces. Our results can be viewed as an extension and refinement of some previous known results in this area.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.393-406
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• 1999

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 second. Radius of con-vergence 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 second Frechet-derivation our radius of convergence results are derived. Results involving superlinear convergence and known to be true or inexact Newton methods are extended here. Moreover we show that under hypotheses on the second Frechet-derivative our radius of conver-gence is larger than the corresponding one in [10]. This allows a wider choice for the initial guess. A numerical example is also pro-vided to show that our radius of convergence is larger then the one in [10].

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.345-360
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• 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].