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Strong approximation of solutions of stochastic differential equations with time-irregular coefficients via randomized euler algorithm

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APPLIED NUMERICAL MATHEMATICS 2014年 78卷 80-94页

作者： Przybylowicz, Pawel Morkisz, Pawel AGH Univ Sci & Technol Fac Appl Math PL-30059 Krakow Poland

We investigate pointwise approximation of the solution of a scalar stochastic differential equation in case when drift coefficient is a Caratheodory mapping and diffusion coefficient is only piecewise Holder continuous with Holder exponent rho is an element of (0, 1 vertical bar. Since under imposed assumptions drift is only measurable with respect to the time variable, the classical euler algorithm does not converge in general to the solution of such equation. We give a construction of the randomized euler scheme and prove that it has the error O(n(-min{rho.1/2})), where n is the number of discretization points. We also investigate the optimality of the defined algorithm. (C) 2013 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Stochastic Caratheodory differential equations euler algorithm euler-integral algorithm Monte Carlo methods Optimal algorithm

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The study of feature extraction of handwritten digits based on euler algorithm

The study of feature extraction of handwritten digits based ...

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International Conference on Advances in Materials Science and Information Technologies in Industry (AMSITI)

作者： Hao Meng-lin Tian Qi-chuan Bai Xue Taiyuan Univ Sci & Technol Taiyuan Peoples R China

ISBN: (纸本)9783038350125

In order to let the computer to recognize the handwritten digits of our lives in common better and faster, on the basis of the advantages of the extraction method in the structural characteristics, this text designed a new characteristics extraction method based on the euler algorithm. With fewer eigenvectors to retain the key information in the topology of 0-9 each of the numeric characters. And to a few special writing figures, we conducted a special simplify processing, easily feature extract, easily identified. Experiments show that, this feature extraction method is simple and effective, saves the time of feature extraction, has somewhat improved the recognition rate compared with other algorithms, was confirmed the effectiveness and practicality of the new algorithm.

关键词： handwritten digits euler algorithm Floral ring Feature extraction

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The study of feature extraction of handwritten digits based on euler algorithm

The study of feature extraction of handwritten digits based ...

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2014 International Conference on Advances in Materials Science and Information Technologies in Industry(AMSITI 2014)

作者： HAO Meng-lin TIAN Qi-chuan BAI Xue Taiyuan University of Science and Technology Beijing University of Civil Engineering & Architecture

In order to let the computer to recognize the handwritten digits of our lives in common better and faster,on the basis of the advantages of the extraction method in the structural characteristics,this text designed a new characteristics extraction method based on the euler *** fewer eigenvectors to retain the key information in the topology of 0-9 each of the numeric *** to a few special writing figures,we conducted a special simplify processing,easily feature extract,easily *** show that,this feature extraction method is simple and effective,saves the time of feature extraction,has somewhat improved the recognition rate compared with other algorithms,was confirmed the effectiveness and practicality of the new algorithm.

关键词： handwritten digits euler algorithm Floral ring Feature extraction

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Image processing applications via time-multiplexing cellular neural network simulator with numerical integration algorithms

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2010年第4期87卷 840-848页

作者： Murugesh, V. European Univ Lefke Dept Comp Engn Trnc Mersin Turkey

A novel approach to simulate cellular neural networks (CNN) is presented in this paper. The approach, time-multiplexing simulation, is prompted by the need to simulate hardware models and test hardware implementations of CNN. For practical applications, due to hardware limitations, it is impossible to have a one-to-one mapping between the CNN hardware processors and all the pixels of the image. This simulator provides a solution by processing the input image block by block, with the number of pixels in a block being the same as the number of CNN processors in the hardware. The algorithm for implementing this simulator is presented along with popular numerical integration algorithms. Some simulation results and comparisons are also presented.

关键词： cellular neural networks euler algorithm RK-Gill algorithm RK-Butcher algorithm ordinary differential equations

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Raster cellular neural network simulator for image processing applications with numerical integration algorithms

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2009年第7期86卷 1215-1221页

作者： Murugesh, V. European Univ Lefke Dept Comp Engn Gemikonagi Lefke Turkey

In this paper, a universal simulator for cellular neural network (CNN) is presented. This simulator is capable of performing Raster simulation for any size of input image, and thus is a powerful tool for researchers investigating potential applications of CNN. This paper reports the latency properties of CNNs along with popular numerical integration algorithms;results and comparisons are also presented.

关键词： cellular neural networks euler algorithm RK-Gill algorithm RK-Butcher algorithm ordinary differential equations

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STABILITY ANALYSIS OF IMPLICIT FINITE-DIFFERENCE SCHEMES FOR PARABOLIC PROBLEMS ON GRAPHS

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NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 2012年第1期33卷 1-20页

作者： Ciegis, R. Tumanova, N. Vilnius Gediminas Tech Univ LT-10223 Vilnius Lithuania

We consider a parabolic problem on branched structures. The Hodgkin-Huxley reaction-diffusion equation is a well-known example of such type models. The diffusion equations on edges of a graph are coupled by two types of conjugation conditions at branch points. The first one describes a conservation of the fluxes at vertexes, and the second conjugation condition defines the conservation of the current flowing at the soma in neuron models. The differential problem is approximated by a theta-implicit finite difference scheme which is based on the theta-method for ODEs. The stability and convergence of the discrete solution is proved in L-2, H-1, and L-infinity norms. The main goal is to estimate the influence of the approximation errors introduced at the branch points of the first type. Results of numerical experiments are presented.

关键词： Convergence Error estimates euler algorithm Finite difference method Graphs Parabolic problem Stability theta-method

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A perishable food supply chain problem considering demand uncertainty and time deadline constraints: Modeling and application to a high-speed railway catering service

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TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2018年 111卷 186-209页

作者： Wu, Xin Nie, Lei Xu, Meng Yan, Fei Beijing Jiaotong Univ Sch Traff & Transportat Beijing 100044 Peoples R China Beijing Jiaotong Univ State Key Lab Rail Traff Control & Safety Beijing 100044 Peoples R China Delft Univ Technol Dept Transport & Planning Delft Netherlands

This paper attempts to optimize the flow patterns in a perishable food supply chain network for a high-speed rail catering service. The proposed variational inequality models describe the uncertain demand on trains using the Newsvendor model and impose time deadline constraints on paths considering flow-dependent lead time. The constraints are then reformulated based on the Dirac delta function so that they can be directly dualized. An euler algorithm with an Augmented Lagrangian Dual algorithm is developed to solve the model. A case study using 246 trains in the Beijing-Shanghai high-speed corridor is applied to demonstrate the applicability of the method.

关键词： Rail catering Variational inequalities Newsvendor model Dirac delta function euler algorithm

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Analyzing Deficient Response Summaries from Designed Experiments

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QUALITY ENGINEERING 2014年第4期26卷 440-449页

作者： Hamada, M. S. Warr, R. L. Los Alamos Natl Lab Los Alamos NM 87545 USA Air Force Inst Technol Dept Math & Stat Dayton OH USA

All too often statisticians do not have access to raw experimental data. These scenarios require additional methodology to properly account for the missing information. In this article, we demonstrate a technique for analyzing averages of lifetime data collected at various experimental conditions that provides inference for factor effects. To handle these summaries, we use some numerical techniques to calculate the probability density function of the average of n independent and identically distributed lognormal random variables. We illustrate our method with an example from the literature and provide some R code that implements a Bayesian analysis. We also provide recommendations for more informative summary statistics than lifetime averages for lognormal data.

关键词： Bayesian inference euler algorithm euler's formula fractional factorial design Laplace transform lifetime lognormal reliability robust design sufficient statistics sum of i.i.d. random variables

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Optimal production strategies of competitive firms considering product innovation

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RAIRO-OPERATIONS RESEARCH 2022年第3期56卷 1335-1352页

作者： Han, Xiaoya Zhou, Yongyi Liu, Xin Univ Shanghai Sci & Technol Business Sch Shanghai 200093 Peoples R China Southeast Univ Sch Econ & Management Nanjing 210096 Peoples R China Elon Univ Love Sch Business Elon NC 27244 USA

Consumer preference for product innovation/functionality has become increasingly diverse, therefore firms produce products with distinct versions/generations to satisfy consumers. This paper investigates the decision-making problem for multiple competitive firms considering consumers' diversified preferences for product functionality. This paper develops an optimization model, in which the profit maximizing firms need to determine the production quantities of their products with different versions. Due to our model's computational complexity, it motivates us to adopt variational inequalities theory, which is applied to convert an original model into a new variational inequality problem. On this basis, the existence and uniqueness of an equilibrium solution are proved, and a high-efficient euler algorithm is proposed. A case study focused on the 5G smartphone market is conducted. Numerical results show that firms may obtain more profits by producing products with newer versions if the consumer preference for product functionality is high. However, if the preference level of consumer is under a certain level, it is not necessarily beneficial for firms who launch new versions of their products to the demand market. In addition, when the competition in market becomes intensive (due to new entrants), giving up the production of previous-version products may be more conducive to existing firms.

关键词： Production strategies product innovation consumer preference competition euler algorithm

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The case for multi-unit single-run descending-price auctions

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ECONOMICS LETTERS 2011年第3期113卷 310-313页

作者： Martinez-Pardina, Irene Romeu, Andres Univ Murcia Fac Econ & Empresa Dpto Fundamentos Anal Econ E-30100 Murcia Spain

We show that a multiple-unit descending-price auction in which the clock is not reset after each sale may be faster and yield more stable prices than an efficient alternative, thus providing sellers a rationale for us... 详细信息

关键词： Multi-unit descending-price sequential auctions Numeric methods euler algorithm

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