论文信息 - Solving Systems of Linear Equations with Relaxed Monte Carlo Method

Solving Systems of Linear Equations with Relaxed Monte Carlo Method

The problem of solving systems of linear algebraic equations by parallel Monte Carlo numerical methods is considered. A parallel Monte Carlo method with relaxation is presented. This is a report of a research in progress, showing the effectiveness of this algorithm. Theoretical justification of this algorithm and numerical experiments are presented. The algorithms were implemented on a cluster of workstations using MPI.

Chih Jeng Kenneth Tan

[1] N. Metropolis,et al. The Monte Carlo method. , 1949 .

[2] J. Hammersley. SIMULATION AND THE MONTE CARLO METHOD , 1982 .

[3] Vassil Alexandrov. Efficient parallel Monte Carlo methods for matrix computations , 1998 .

[4] H. Kahn. Random sampling (Monte Carlo) techniques in neutron attenuation problems--II. , 1950, Nucleonics.

[5] John N. Tsitsiklis,et al. Parallel and distributed computation , 1989 .

[6] J. A. Rod Blais,et al. PLFG: A Highly Scalable Parallel Pseudo-random Number Generator for Monte Carlo Simulations , 2000, HPCN Europe.

[7] D. Faddeev,et al. Computational methods of linear algebra , 1981 .

[8] J. Westlake. Handbook of Numerical Matrix Inversion and Solution of Linear Equations , 1968 .

[9] I. Dimov,et al. A new iterative Monte Carlo approach for inverse matrix problem , 1998 .

[10] H. Kahn,et al. Random sampling (Monte Carlo) techniques in neutron attenuation problems--I. , 1950, Nucleonics.

[11] D. Faddeev,et al. Computational Methods of Linear Algebra , 1959 .

[12] R. A. Leibler,et al. Matrix inversion by a Monte Carlo method , 1950 .

[13] Chih Jeng Kenneth Tan,et al. Efficient Monte Carlo Linear Solver with Chain Reduction and Optimization Using PLFG , 2001, HPCN Europe.

[14] Ivan Dimov,et al. Random walk on distant mesh points Monte Carlo methods , 1993 .

[15] Graham M. Megson,et al. Systolic Matrix Inversion Using a Monte Carlo Method , 1994, Parallel Algorithms Appl..