Accuracy of Monte Carlo Method for Solution of Linear Algebraic Equations Using PLFG and Rand()

Computational Science — ICCS 2001

Alexandrov

2001

Self Cite

Abstract. 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.

Section: Relaxed Monte Carlo Methodsmentioning

confidence: 99%

“…The stochastic error, , and the deterministic error parameters were both set to 0.01. The PLFG parallel pseudo-random number generator [17] was used as the source of randomness for the experiments conducted. The time to solution given in the tables is the actual computation time, in seconds.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Relaxed Monte Carlo Linear Solver

Computational Science — ICCS 2001

Alexandrov

2001

Self Cite

“…The stochastic error, , and the deterministic error parameters were both set to 0.01. The PLFG parallel pseudorandom number generator [17] was used as the source of randomness for the experiments conducted.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Antithetic Monte Carlo Linear Solver

Lecture Notes in Computer Science

2002

Self Cite

The problem of solving systems of linear algebraic equations by parallel Monte Carlo numerical methods is considered. A parallel Monte Carlo method with relaxation parameter and dispersion reduction using antithetic variates 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. Keyword: Monte Carlo method, Linear solver, Systems of linear algebraic equations, Parallel algorithms. Now at SHARCNET,

“…It is clear that the PLFG parallel pseudo-random number generator gives superior results compared to the results obtained by parallel pseudo-random number generators provided in the Scalable Pseudo-random Number Generator (SPRNG) package developed at the National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign. PLFG has also been put to test, against the multiplicative lagged Fibnacci generator from the SPRNG package, using the Relaxed Monte Carlo method for solving of systems of linear algebraic equations [10]. Comparing the results shown in Tables 3 and 4, it is clear that PLFG is at least on par with the multiplicative lagged Fibnacci generator from the SPRNG package, if not a better parallel pseudo-random number generator.…”

Section: Quality Of Sequences Generatedmentioning

confidence: 99%

On Parallel Pseudo-Random Number Generation

Computational Science — ICCS 2001

2001

Self Cite

Abstract. Parallel computing has been touted as the pinnacle of high performance digital computing by many. However, many problems remain intractable using deterministic algorithms. Randomized algorithms which are, in some cases, less efficient than their deterministic counterpart for smaller problem sizes, can overturn the intractability of various large scale problems. These algorithms, however, require a source of randomness. Pseudo-random number generators were created for many of these purposes. When performing computations on parallel machines, an additional criterion for randomized algorithms to be worthwhile is the availability of a parallel pseudo-random number generator. This paper presents an efficient algorithm for parallel pseudo-random number generation.