• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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• pp.133-139
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• 2006

By combining the classical Newton's method with the pseudo-secant method, pseudo-secant-Newton's method is constructed and its order and rate of convergence are investigated. Given a function $f:\mathbb{R}{\rightarrow}\mathbb{R}$ that has a simple real zero ${\alpha}$ and is sufficiently smooth in a small neighborhood of ${\alpha}$, the convergence behavior is analyzed near ${\alpha}$ for pseudo-secant-Newton's method. The order of convergence is shown to be cubic and the rate of convergence is proven to be $\(\frac{f^{{\prime}{\prime}}(\alpha)}{2f^{\prime}(\alpha)}\)^2$. Numerical experiments show the validity of the theory presented here and are confirmed via high-precision programming in Mathematica.

• 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.

• 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.

• Journal of Integrative Natural Science
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• v.6 no.1
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• pp.53-56
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• 2013

We are interested in the rate of convergence of solutions of 2D Navier-Stokes equations in a smooth bounded domain as the viscosity tends to zero under Navier friction condition. If the initial velocity is smooth enough($u{\in}W^{2,p}$, p>2), it is known that the rate of convergence is linearly propotional to the viscosity. Here, we consider the rate of convergence for nonsmooth velocity fields when the gradient of the corresponding solution of the Euler equations belongs to certain Orlicz spaces. As a corollary, if the initial vorticity is bounded and small enough, we obtain a sublinear rate of convergence.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.125-130
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• 2007

We propose a simple and intuitive method to derive the exact convergence rate of global $L_{2}-norm$ error for strong numerical approximation of stochastic differential equations the result of which has been reported by Hofmann and $M{\"u}ller-Gronbach\;(2004)$. We conclude that any strong numerical scheme of order ${\gamma}\;>\;1/2$ has the same optimal convergence rate for this error. The method clearly reveals the structure of global $L_{2}-norm$ error and is similarly applicable for evaluating the convergence rate of global uniform approximations.

• 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.

• 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 the Korean Society of Manufacturing Process Engineers
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• v.21 no.9
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• pp.92-97
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• 2022

In this paper, as a research on autonomous steering for agriculture, a sensor module for furrow recognition was developed through a low-cost distance sensor combination. The developed sensor module was applied to the vehicle, and when driving in a furrow curve, the autonomous steering success rate was 100% at a curvature of 20 m or more, and 70% at a curvature of 15 m or less. The self-steering success rate according to the ground condition showed a 100% success rate regardless of soil, weeds, or mulching film.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.8
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• pp.3749-3768
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• 2018

As one of the most potential types of low-density parity-check (LDPC) codes, CPM-QC-LDPC code has considerable advantages but there still exist some limitations in practical application, for example, the existing decoding algorithm has a low convergence rate and a high decoding complexity. According to the structural property of this code, we propose a new method based on a CPM-RID decoding algorithm that decodes block-by-block with weights, which are obtained by neural network training. From the simulation results, we can conclude that our proposed method not only improves the bit error rate and frame error rate performance but also increases the convergence rate, when compared with the original CPM-RID decoding algorithm and scaled MSA algorithm.