• Journal of the Korean Data and Information Science Society
• /
• v.14 no.4
• /
• pp.929-937
• /
• 2003

Kernel type estimations of discontinuity point at an unknown location in regression function or its derivatives have been developed. It is known that the discontinuity point estimator based on $Gasser-M\ddot{u}ller$ regression estimator with a one-sided kernel function which has a zero value at the point 0 makes a poor asymptotic behavior. Further, the asymptotic variance of $Gasser-M\ddot{u}ller$ regression estimator in the random design case is 1.5 times larger that the one in the corresponding fixed design case, while those two are identical for the local polynomial regression estimator. Although $Gasser-M\ddot{u}ller$ regression estimator with a one-sided kernel function which has a non-zero value at the point 0 for the modification is used, computer simulation show that this phenomenon is also appeared in the discontinuity point estimation.

• Honam Mathematical Journal
• /
• v.35 no.2
• /
• pp.235-249
• /
• 2013

It is well known that each kernel function defines primal-dual interior-point method (IPM). Most of polynomial-time interior-point algorithms for linear optimization (LO) are based on the logarithmic kernel function ([9]). In this paper we define new eligible kernel function and propose a new search direction and proximity function based on this function for LO problems. We show that the new algorithm has $\mathcal{O}(({\log}\;p)^{\frac{5}{2}}\sqrt{n}{\log}\;n\;{\log}\frac{n}{\epsilon})$ and $\mathcal{O}(q^{\frac{3}{2}}({\log}\;p)^3\sqrt{n}{\log}\;\frac{n}{\epsilon})$ iteration complexity for large- and small-update methods, respectively. These are currently the best known complexity results for such methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.13 no.1
• /
• pp.41-53
• /
• 2009

A primal-dual interior point method(IPM) not only is the most efficient method for a computational point of view but also has polynomial complexity. Most of polynomialtime interior point methods(IPMs) are based on the logarithmic barrier functions. Peng et al.([14, 15]) and Roos et al.([3]-[9]) proposed new variants of IPMs based on kernel functions which are called self-regular and eligible functions, respectively. In this paper we define a new kernel function and propose a new IPM based on this kernel function which has $O(n^{\frac{2}{3}}log\frac{n}{\epsilon})$ and $O(\sqrt{n}log\frac{n}{\epsilon})$ iteration bounds for large-update and small-update methods, respectively.

• East Asian mathematical journal
• /
• v.26 no.1
• /
• pp.9-23
• /
• 2010

In this paper we generalize large-update primal-dual interior point methods for linear optimization problems in [2] to the $P_*(\kappa)$ linear complementarity problems based on a new kernel function which includes the kernel function in [2] as a special case. The kernel function is neither self-regular nor eligible. Furthermore, we improve the complexity result in [2] from $O(\sqrt[]{n}(\log\;n)^2\;\log\;\frac{n{\mu}o}{\epsilon})$ to $O\sqrt[]{n}(\log\;n)\log(\log\;n)\log\;\frac{m{\mu}o}{\epsilon}$.

• Journal of Radiation Industry
• /
• v.17 no.3
• /
• pp.275-282
• /
• 2023

Workers in nuclear power plants are likely to be exposed to radiation from various geometrical sources. In order to evaluate the exposure level, the point-kernel method can be utilized. In order to perform a dose assessment based on this method, the radiation source should be divided into point sources, and the number of divisions should be set by the evaluator. However, for the general public, there may be difficulties in selecting the appropriate number of divisions and performing an evaluation. Therefore, the purpose of this study is to develop an algorithm for dose assessment for arbitrary shaped sources based on the point-kernel method. For this purpose, the point-kernel method was analyzed and the main factors for the dose assessment were selected. Subsequently, based on the analyzed methodology, a dose assessment algorithm for arbitrary shaped sources was developed. Lastly, the developed algorithm was verified using Microshield. The dose assessment procedure of the developed algorithm consisted of 1) boundary space setting step, 2) source grid division step, 3) the set of point sources generation step, and 4) dose assessment step. In the boundary space setting step, the boundaries of the space occupied by the sources are set. In the grid division step, the boundary space is divided into several grids. In the set of point sources generation step, the coordinates of the point sources are set by considering the proportion of sources occupying each grid. Finally, in the dose assessment step, the results of the dose assessments for each point source are summed up to derive the dose rate. In order to verify the developed algorithm, the exposure scenario was established based on the standard exposure scenario presented by the American National Standards Institute. The results of the evaluation with the developed algorithm and Microshield were compare. The results of the evaluation with the developed algorithm showed a range of 1.99×10^-1~9.74×10^-1 μSv hr^-1, depending on the distance and the error between the results of the developed algorithm and Microshield was about 0.48~6.93%. The error was attributed to the difference in the number of point sources and point source distribution between the developed algorithm and the Microshield. The results of this study can be utilized for external exposure radiation dose assessments based on the point-kernel method.

• Journal of the Korean Statistical Society
• /
• v.31 no.2
• /
• pp.261-276
• /
• 2002

Probability density or its derivatives may have a discontinuity/change point at an unknown location. We propose a method of estimating the location and the jump size of the discontinuity point based on kernel type density or density derivatives estimators with one-sided equivalent kernels. The rates of convergence of the proposed estimators are derived, and the finite-sample performances of the methods are illustrated by simulated examples.

• Journal of the Korean Statistical Society
• /
• v.33 no.1
• /
• pp.59-78
• /
• 2004

A regression function in generalized linear model may have a discontinuity/change point at unknown location. In order to estimate the location of the discontinuity point and its jump size, the strategy is to use a nonparametric approach based on one-sided kernel weighted local-likelihood functions. Weak convergences of the proposed estimators are established. The finite-sample performances of the proposed estimators with practical aspects are illustrated by simulated examples.

• East Asian mathematical journal
• /
• v.29 no.3
• /
• pp.279-292
• /
• 2013

It is well known that each kernel function defines a primal-dual interior-point method(IPM). Most of polynomial-time interior-point algorithms for linear optimization(LO) are based on the logarithmic kernel function([2, 11]). In this paper we define a new eligible kernel function and propose a new search direction and proximity function based on this function for LO problems. We show that the new algorithm has ${\mathcal{O}}((log\;p){\sqrt{n}}\;log\;n\;log\;{\frac{n}{\epsilon}})$ and ${\mathcal{O}}((q\;log\;p)^{\frac{3}{2}}{\sqrt{n}}\;log\;{\frac{n}{\epsilon}})$ iteration bound for large- and small-update methods, respectively. These are currently the best known complexity results.

• The Pure and Applied Mathematics
• /
• v.21 no.1
• /
• pp.51-60
• /
• 2014

In this paper, we construct a complex reproducing kernel space for singular multi-point BVPs, and skillfully obtain reproducing kernel expressions. Then, we transform the problem into an equivalent operator equation, and give a numerical algorithm to provide the approximate solution. The uniform convergence of this algorithm is proved, and complexity analysis is done. Lastly, we show the validity and feasibility of the numerical algorithm by two numerical examples.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.13 no.3
• /
• pp.189-202
• /
• 2009

In this paper we propose new primal-dual interior point algorithms for $P_*(\kappa)$ linear complementarity problems based on a new class of kernel functions which contains the kernel function in [8] as a special case. We show that the iteration bounds are $O((1+2\kappa)n^{\frac{9}{14}}\;log\;\frac{n{\mu}^0}{\epsilon}$) for large-update and $O((1+2\kappa)\sqrt{n}log\frac{n{\mu}^0}{\epsilon}$) for small-update methods, respectively. This iteration complexity for large-update methods improves the iteration complexity with a factor $n^{\frac{5}{14}}$ when compared with the method based on the classical logarithmic kernel function. For small-update, the iteration complexity is the best known bound for such methods.