• Journal of applied mathematics & informatics
• /
• 제7권1호
• /
• pp.223-236
• /
• 2000

In this paper, we solve the Fredholm integral equation of the first and second kind when the kernel takes a singular form. Also, some important relations for Chebyshev polynomial of integration are established.

• Journal of applied mathematics & informatics
• /
• 제12권1_2호
• /
• pp.165-182
• /
• 2003

Toeplitz matrix method and the product Nystrom method are described for mixed Fredholm-Volterra singular integral equation of the second kind with Carleman Kernel and logarithmic kernel. The results are compared with the exact solution of the integral equation. The error of each method is calculated.

• 대한수학회지
• /
• 제33권4호
• /
• pp.929-954
• /
• 1996

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제7권2호
• /
• pp.65-73
• /
• 2003

In this work, we use a numerical method to solve the nonlinear integral equation of the second kind when the kernel of the integral equation in the logarithmic function form or in Carleman function form. The solution has a computing time requirement of $0(N^2)$, where (2N +1) is the number of discretization points used. Also, the error estimate is computed.

• 호남수학학술지
• /
• 제35권2호
• /
• 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
• /
• 제13권1호
• /
• 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
• /
• 제29권3호
• /
• 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.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제13권3호
• /
• 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.

• Communications for Statistical Applications and Methods
• /
• 제21권2호
• /
• pp.115-124
• /
• 2014

In this paper we derive a Berry-Esseen type bound for the kernel density estimator of a random left truncated model, in which each datum (Y) is randomly left truncated and is sampled if $Y{\geq}T$, where T is the truncation random variable with an unknown distribution. This unknown distribution is estimated with the Lynden-Bell estimator. In particular the normal approximation rate, by choice of the bandwidth, is shown to be close to $n^{-1/6}$ modulo logarithmic term. We have also investigated this normal approximation rate via a simulation study.

• 한국통신학회논문지
• /
• 제19권2호
• /
• pp.225-230
• /
• 1994

전자장 해석을 위한 많은 수식들이 전계형 적분방정식으로 수식화되어 여러 가지 수치적인 방법으로 해석되어진다. 일반적으로 이 식은 특이점을 갖는 Kernel로 표현되어지며, 주어진 문제에 따라 식이 간략화 되어지지 않으면 해석시 수직과 프로그램이 복잡하여진다. 본 논문에서는 BOR구조의 도체에 적용할 수 있는 새로운 적분방정식을유도하였으며, 이 식은 직선형 wire도체의 경우에 더욱 간략화 되어진다. 동축선로로 급전되어지는 monopole안테나와 임의의 각도로 입사하는 평면파에 의한 도체의 산란문제를 응용예로서 다루었다.