scholarly journals GPU-Based Monte Carlo Methods for Solving Linear Algebraic Equations

2016 ◽  
Author(s):  
Siyan Lai
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Algebraic Equations ◽  
Linear Algebraic Equations

scholarly journals A new method for solving a class of heat conduction equations

2015 ◽  
Vol 19 (4) ◽  
pp. 1205-1210
Author(s):  
Yi Tian ◽  
Zai-Zai Yan ◽  
Zhi-Min Hong
Keyword(s):  
Monte Carlo ◽  
Heat Conduction ◽  
Dimensional Space ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Governing Equations ◽  
One Dimensional ◽  
Sparse System ◽  
Linear Algebraic Equations ◽  
Crank Nicolson

A numerical method for solving a class of heat conduction equations with variable coefficients in one dimensional space is demonstrated. This method combines the Crank-Nicolson and Monte Carlo methods. Using Crank-Nicolson method, the governing equations are discretized into a large sparse system of linear algebraic equations, which are solved by Monte Carlo method. To illustrate the usefulness of this technique, we apply it to two problems. Numerical results show the performance of the present work.

scholarly journals Monte Carlo method for solving a parabolic problem

2016 ◽  
Vol 20 (3) ◽  
pp. 933-937
Author(s):  
Yi Tian ◽  
Zai-Zai Yan
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Random Sampling ◽  
Parabolic Problem ◽  
Test Problems ◽  
Algebraic Equations ◽  
Governing Equations ◽  
Sparse System ◽  
Linear Algebraic Equations ◽  
Crank Nicolson

In this paper, we present a numerical method based on random sampling for a parabolic problem. This method combines use of the Crank-Nicolson method and Monte Carlo method. In the numerical algorithm, we first discretize governing equations by Crank-Nicolson method, and obtain a large sparse system of linear algebraic equations, then use Monte Carlo method to solve the linear algebraic equations. To illustrate the usefulness of this technique, we apply it to some test problems.

Sequential Monte Carlo

1962 ◽  
Vol 58 (1) ◽  
pp. 57-78 ◽  
Author(s):  
J. H. Halton
Keyword(s):  
Monte Carlo ◽  
Sequential Monte Carlo ◽  
Algebraic Equations ◽  
Sequential Method ◽  
Von Neumann ◽  
Linear Algebraic Equations ◽  
Sequential Processes

ABSTRACTThis paper defines the concept of sequential Monte Carlo and outlines the principal modes of approach which may be expected to yield useful sequential processes. Three workable sequential processes, derived from a non-sequential method of J. von Neumann and S. M. Ulam for solving systems of linear algebraic equations, are described and analysed in detail.

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