Abstract
In this paper, the accuracy of the results of Monte Carlo method for solution of linear algebraic equations obtained using a parallel pseudo-random generator, named PLFG, is compared to that of the popular rand() serial pseudo-random generator found in most ANSI Standard C implementations. PLFG is designed for MIMD architectures, implemented using Message Passing Interface (MPI) in C. It is highly scalable and with the default parameters chosen, it provides an astronomical period of at least 229 (223209 – l). Results from numerical experiments show that a simple change of the randomness source, from rand() to PLFG will give much better estimates of the solution vector.
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References
Alexandrov, V. N. (1998). Efficient Parallel Monte Carlo Methods for Matrix Computations. Mathematics and Computers in Simulation, 47.
Bertsekas, D. P. and Tsitsiklis, J. N. (1997). Parallel and Distributed Computation: Numerical Methods. Athena Scientific.
Coddington, P. D. (1994). Analysis of Random Number Generators Using Monte Carlo Simulation. International Journal of Modern Physics, C5.
Coddington, P. D. (1997). Random Number Generators for Parallel Computers. National HPCC Software Exchange Review, (1.1).
Dimov, I. T. (1991). Minimization of the Probable Error for some Monte Carlo Methods. In Dimov, I. T., Andreev, A. S., Markov, S. M., and Ullrich, S., editors, Mathematical Modelling and Scientific Computations, pages 159–170. Publication House of the Bulgarian Academy of Science.
Eichenauer-Herrmann, J. and Grothe, H. (1989). A Remark on Long-range Correlation in Multiplicative Congruential Pseudo-random Number Generators. Numerical Mathematics, 56.
Knuth, D. E. (1998). The Art of Computer Programming, Volume II: Seminumerical Algorithms. Addison Wesley Longman Higher Education, 3 edition.
Lagarias, J. C. (1990). Pseudorandom Number Generators in Cryptography and Number Theory. In Pomerance, C., editor, Cryptology and Computational Number Theory, volume 42 of Proceedings of Symposia in Applied Mathematics, pages 115–145. American Mathematical Society.
Lehmer, D. H. (1949). Mathematical Methods in Large-scale Computing Units. In Proceedings of the 2nd. Symposium on Large Scale Digital Calculating Machinery. Harvard University Press.
Marsaglia, G. (1984). A Current View of Random Number Generators. In Computing Science and Statistics: Proceedings of the XVI Symposium on the Interface.
Mascagni, M., Ceperley, D., and Srinivasan, A. (1999). SPRNG: A Scalable Library for Pseudorandom Number Generation. In Spanier, J., editor, Proceedings of the Third International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing. Springer Verlag.
Mascagni, M., Cuccaro, S. A., Pryvor, D. V., and Robinson, M. L. (1995a). A Fast, High Quality, and Reproducible Parallel Lagged-Fibonacci Pseudorandom Number Generator. Journal of Computational Physics, 119:211–219.
Mascagni, M., Cuccaro, S. A., Pryvor, D. V., and Robinson, M. L. (1995b). Parallel Pseudorandom Number Generation Using Additive Lagged-Fibonacci Recursions. In Lecture Notes in Statistics, volume 106, pages 263–277. Springer Verlag.
Mascagni, M., Cuccaro, S. A., Pryvor, D. V., and Robinson, M. L. (1995c). Recent Developments in Parallel Pseudorandom Number Generation. In Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing.
Matsumoto, M. and Nishimura, T. (1998). Mersenne Twister: A 623-Di-mensionally Equidistributed Uniform Pseudo-Random Number Generator. ACM Transactions on Modeling and Computer Simulation, 8(1).
Rubinstein, R. Y. (1981). Simulation and the Monte Carlo Method. John Wiley and Sons.
Sobol’, I. M. (1973). Monte Carlo Numerical Methods. Moscow, Nauka. (In Russian.).
Srinivasan, A., Ceperley, D., and Mascagni, M. (1998). Testing Parallel Random Number Generators. In Proceedings of the Third International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing.
Tan, C. J. K. and Blais, J. A. R. (2000). PLFG: A Highly Scalable Parallel Pseudo-random Number Generator for Monte Carlo Simulations. In Bubak, M., Afsarmanesh, H., Williams, R., and Hertzberger, B., editors, High Performance Computing and Networking, Proceedings of the 8th International Conference on High Performance Computing and Networking Europe, volume 1823 of Lecture Notes in Computer Science, pages 127–135. Springer Verlag.
Vattulainen, I., Ala-Nissila, T., and Kankaala, K. (1995). Physical Models as Tests of Randomness. Physics Review, E52.
Westlake, J. R. (1968). A Handbook of Numerical Matrix Inversion and Solution of Linear Equations. John Wiley and Sons.
Williams, K. P. and Williams, S. A. (1995). Implementation of an Efficient and Powerful Parallel Pseudo-random Number Generator. In Proceedings of the Second European PVM Users’ Group Meeting.
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Tan, C.J.K., Villalba, M.I.C., Alexandrov, V. (2002). Accuracy of Monte Carlo Method for Solution of Linear Algebraic Equations Using PLFG and Rand(). In: Dimopoulos, N.J., Li, K.F. (eds) High Performance Computing Systems and Applications. The Kluwer International Series in Engineering and Computer Science, vol 657. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0849-6_7
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DOI: https://doi.org/10.1007/978-1-4615-0849-6_7
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