求解高维问题的组合概率算法

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-01-02 DOI:10.1080/17442508.2014.914515

R. Farnoosh, Mahboubeh Aalaei, M. Ebrahimi

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引用次数: 2

摘要

本文建立了一种基于蒙特卡罗(MC)模拟的高维线性代数方程组(LSAEs)和二维第二类Fredholm积分方程(FIESK)的精确、高效的求解算法。基于Jacobi过松弛法和MC模拟，结合迭代细化技术，提出了一种新的数值-概率组合算法，用于求解大型稀疏lsae的唯一解。它具有精度好、成本低、结构简单等优点。理论结果证明了算法的收敛性。为了验证本文工作的准确性和效率，将所提出的算法用于求解和lsae。此外，将该算法与Galerkin方法相结合，说明了该算法求解二维FIESK的能力和有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Combined probabilistic algorithm for solving high dimensional problems

The present study establishes an accurate and efficient algorithm based on Monte Carlo (MC) simulation for solving high dimensional linear systems of algebraic equations (LSAEs) and two-dimensional Fredholm integral equations of the second kind (FIESK). This new combined numerical-probabilistic algorithm is based on Jacobi over-relaxation method and MC simulation in conjunction with the iterative refinement technique to find the unique solution of the large sparse LSAEs. It has an excellent accuracy, low cost and simple structure. Theoretical results are established to justify the convergence of the algorithm. To confirm the accuracy and efficiency of the present work, the proposed algorithm is used for solving and LSAEs. Furthermore, the algorithm is coupled with Galerkin's method to illustrate the power and effectiveness of the proposed algorithm for solving two-dimensional FIESK.

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来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.