• 제목/요약/키워드: laplace approximation

검색결과 29건 처리시간 0.029초

z변환을 이용한 시간영역에서의 승차감 평가 (Evaluation of Ride Comfort in Time Domain by Using z-Transform)

  • 김영국;김석원;박찬경;김상수;김기환
    • 한국철도학회논문집
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    • 제14권6호
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    • pp.495-500
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    • 2011
  • 철도차량의 승차감은 승객이 느끼는 감정이므로 물리적인 진동의 크기뿐만 아니라 인간의 감응도(느낌)도 고려하여야 하며, 이러한 진동에 대한 인간의 감응도를 나타낸 것이 주파수 보정곡선이다. 주파수 보정곡선은 라플라스 변환형태의 전달함수이기 때문에 이 전달함수를 직접 사용하여 시간 영역에서의 승차감의 평가가 불가능하다. 이를 해결하기 위해서 본 논문에서는 라플라스 변환형태의 전달함수를 시간 영역에서 사용할 수 있는 전달함수로 변환하는 방법을 제시하고 다양한 예제를 통해 이 방법에 대한 타당성을 입증하였다.

ML estimation using Poisson HGLM approach in semi-parametric frailty models

  • Ha, Il Do
    • Journal of the Korean Data and Information Science Society
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    • 제27권5호
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    • pp.1389-1397
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    • 2016
  • Semi-parametric frailty model with nonparametric baseline hazards has been widely used for the analyses of clustered survival-time data. The frailty models can be fitted via an auxiliary Poisson hierarchical generalized linear model (HGLM). For the inferences of the frailty model marginal likelihood, which gives MLE, is often used. The marginal likelihood is usually obtained by integrating out random effects, but it often requires an intractable integration. In this paper, we propose to obtain the MLE via Laplace approximation using a Poisson HGLM approach for semi-parametric frailty model. The proposed HGLM approach uses hierarchical-likelihood (h-likelihood), which avoids integration itself. The proposed method is illustrated using a numerical study.

A New Approach for the Derivation of a Discrete Approximation Formula on Uniform Grid for Harmonic Functions

  • Kim, Philsu;Choi, Hyun Jung;Ahn, Soyoung
    • Kyungpook Mathematical Journal
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    • 제47권4호
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    • pp.529-548
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    • 2007
  • The purpose of this article is to find a relation between the finite difference method and the boundary element method, and propose a new approach deriving a discrete approximation formula as like that of the finite difference method for harmonic functions. We develop a discrete approximation formula on a uniform grid based on the boundary integral formulations. We consider three different boundary integral formulations and derive one discrete approximation formula on the uniform grid for the harmonic function. We show that the proposed discrete approximation formula has the same computational molecules with that of the finite difference formula for the Laplace operator ${\nabla}^2$.

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Comparison of Alternate Approaches for Reversible Geminate Recombination

  • Khokhlova, Svetlana S.;Agmon, Noam
    • Bulletin of the Korean Chemical Society
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    • 제33권3호
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    • pp.1020-1028
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    • 2012
  • This work compares various models for geminate reversible diffusion influenced reactions. The commonly utilized contact reactivity model (an extension of the Collins-Kimball radiation boundary condition) is augmented here by a volume reactivity model, which extends the celebrated Feynman-Kac equation for irreversible depletion within a reaction sphere. We obtain the exact analytic solution in Laplace space for an initially bound pair, which can dissociate, diffuse or undergo "sticky" recombination. We show that the same expression for the binding probability holds also for "mixed" reaction products. Two different derivations are pursued, yielding seemingly different expressions, which nevertheless coincide numerically. These binding probabilities and their Laplace transforms are compared graphically with those from the contact reactivity model and a previously suggested coarse grained approximation. Mathematically, all these Laplace transforms conform to a single generic equation, in which different reactionless Green's functions, g(s), are incorporated. In most of parameter space the sensitivity to g(s) is not large, so that the binding probabilities for the volume and contact reactivity models are rather similar.

On the Numerical Inversion of the Laplace Transform by the Use of an Optimized Legendre Polynomial

  • Al-Shuaibi, Abdulaziz
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • 제4권1호
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    • pp.49-65
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    • 2000
  • A method for inverting the Laplace transform is presented, using a finite series of the classical Legendre polynomials. The method recovers a real-valued function f(t) in a finite interval of the positive real axis when f(t) belongs to a certain class ${\mathcal{W}}_{\beta}$ and requires the knowledge of its Laplace transform F(s) only at a finite number of discrete points on the real axis s > 0. The choice of these points will be carefully considered so as to improve the approximation error as well as to minimize the number of steps needed in the evaluations. The method is tested on few examples, with particular emphasis on the estimation of the error bounds involved.

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SEMIGROUP OF LIPSCHITZ OPERATORS

  • Lee, Young S.
    • Korean Journal of Mathematics
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    • 제14권2호
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    • pp.273-280
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    • 2006
  • Lipschitzian semigroup is a semigroup of Lipschitz operators which contains $C_0$ semigroup and nonlinear semigroup. In this paper, we establish the cannonical exponential formula of Lipschitzian semigroup from its Lie generator and the approximation theorem by Laplace transform approach to Lipschitzian semigroup.

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Non-Simultaneous Sampling Deactivation during the Parameter Approximation of a Topic Model

  • Jeong, Young-Seob;Jin, Sou-Young;Choi, Ho-Jin
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • 제7권1호
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    • pp.81-98
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    • 2013
  • Since Probabilistic Latent Semantic Analysis (PLSA) and Latent Dirichlet Allocation (LDA) were introduced, many revised or extended topic models have appeared. Due to the intractable likelihood of these models, training any topic model requires to use some approximation algorithm such as variational approximation, Laplace approximation, or Markov chain Monte Carlo (MCMC). Although these approximation algorithms perform well, training a topic model is still computationally expensive given the large amount of data it requires. In this paper, we propose a new method, called non-simultaneous sampling deactivation, for efficient approximation of parameters in a topic model. While each random variable is normally sampled or obtained by a single predefined burn-in period in the traditional approximation algorithms, our new method is based on the observation that the random variable nodes in one topic model have all different periods of convergence. During the iterative approximation process, the proposed method allows each random variable node to be terminated or deactivated when it is converged. Therefore, compared to the traditional approximation ways in which usually every node is deactivated concurrently, the proposed method achieves the inference efficiency in terms of time and memory. We do not propose a new approximation algorithm, but a new process applicable to the existing approximation algorithms. Through experiments, we show the time and memory efficiency of the method, and discuss about the tradeoff between the efficiency of the approximation process and the parameter consistency.

DEFAULTABLE BOND PRICING USING REGIME SWITCHING INTENSITY MODEL

  • Goutte, Stephane;Ngoupeyou, Armand
    • Journal of applied mathematics & informatics
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    • 제31권5_6호
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    • pp.711-732
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    • 2013
  • In this paper, we are interested in finding explicit numerical formulas to evaluate defaultable bonds prices of firms. For this purpose, we use a default intensity whose values depend on the credit rating of these firms. Each credit rating corresponds to a state of the default intensity. Then, this regime switches as soon as one of the credit rating of a firm also changes. Moreover, this regime switching default intensity model allows us to capture well some market features or economics behaviors. Thus, we obtain two explicit different formulas to evaluate the conditional Laplace transform of a regime switching Cox Ingersoll Ross model. One using the property of semi-affine of the model and the other one using analytic approximation. We conclude by giving some numerical illustrations of these formulas and real data estimation results.

Investigation on the Analysis of Transmission Line with Frequency Dependent Lossy Term

  • Ichikawa, Satoshi
    • 대한전자공학회:학술대회논문집
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    • 대한전자공학회 2002년도 ITC-CSCC -1
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    • pp.650-653
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    • 2002
  • The increaseing speeds are accompanied by decreases in pulse rise and fall time in VLSI circuits. These accenturate the high frequency spectral contents of the signals and cause the frequency dependent loss of the conductors which interconnect the various sub-circuits composing of VLSI circuit. The lossy effect is approximated by the square root of frequency dependence of the per unit length resistance. In the practical applications, several problems may arise along with this approximation, so we extend our investigation of the lossy effect by numerical Laplace inversion method.

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ENHANCING EIGENVALUE APPROXIMATION WITH BANK-WEISER ERROR ESTIMATORS

  • Kim, Kwang-Yeon
    • Korean Journal of Mathematics
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    • 제28권3호
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    • pp.587-601
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    • 2020
  • In this paper we propose a way of enhancing eigenvalue approximations with the Bank-Weiser error estimators for the P1 and P2 conforming finite element methods of the Laplace eigenvalue problem. It is shown that we can achieve two extra orders of convergence than those of the original eigenvalue approximations when the corresponding eigenfunctions are smooth and the underlying triangulations are strongly regular. Some numerical results are presented to demonstrate the accuracy of the enhanced eigenvalue approximations.