Parallel quasi-Monte Carlo methods for Linear Algebra problems

Monte Carlo Methods and Applications

Volumn 10, Issue 3-4, 2004, Pages 213-219

  Alexandrov, V ^a   Atanassov, E ^b   Dimov, I ^b  

^a UNIVERSITY OF READING   (United Kingdom)

^b BULGARIAN ACADEMY OF SCIENCES   (Bulgaria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746649718     PISSN: 09299629     EISSN: 15693961     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (16)

1. E. I. Atanassov, New Efficient Algorithm for Generating the Sobol Sequences with Scrambling, Numerical Methods and Applications, Borovets 2002, Lecture Notes in Computer Science, Vol. 2542 (2003), Springer-Verlag, pp. 83-90.
2. E. I. Atanassov, M. K. Durtchova, Generating and Testing the Modified Halton Sequences, Numerical Methods and Applications, Borovets 2002, LNCS 2542, Springer-Verlag, 2003, pp. 91-98.
3. R. C. Baker, On irregularities of distribution II, J. London Math. Soc. (2) 59 (1999), pp. 50-64
4. Curtiss J.H. A Theoretical Comparison of the Efficiencies of two classical methods and a Monte Carlo method for Computing one component of the solution of a set of Linear Algebraic Equations, Proc. Symposium on Monte Carlo Methods, John Wiley and Sons, 1956, pp. 191-233.
5. Dimov LT. Minimization of the probable error for some Monte Carlo methods, Proc. of the Summer School on Mathematical Modelling and Scientific Computations, 23-28.09.1990, Albena, Bulgaria, Publ. House of the Bulg. Acad. Sei., 1991, pp. 159-170.
6. I. Dimov, Efficient and Overconvergent Monte Carlo Methods, Addvances in Parallel Algorithms, IOS Press, Amsterdam, 1994, pp. 100-111.
7. I. Dimov, V. Alexandrov, A. Karaivanova, Parallel resolvent Monte Carlo algorithms for linear algebra problems, Mathematics and Computers in Simulation, Vol. 55 (2001), pp. 25-35 (Pubitemid 32672704)
8. M. Mascagni, A. Karaivanova, Matrix Computations using quasirandom sequences, in Numerical Analysis and its Applications, Lecture Notes in Computer Science, Vol. 1988 (2001), Springer, pp. 552-559. (Pubitemid 33242287)
9. M. Mascagni, SPRNG: A Scalable Library for Pseudorandom Number Generation, in: 0. Hiev, M. Kaschiev, Bl. Sendov, P.S. Vassilevski eds., Recent Advances in Numerical Methods and Applications II, Proceeding of NMA 1998, World Scientific, Singapore, 1999, pp. 284-295.
10. A. Karaivanova, R. Georgieva, Solving Systems of Linear Algebraic Equations using Quasi-Random Numbers, Third International Conference on Large Scale Scientific Computing, Sozopol, Bulgaria, June 2001, Springer Verlag, LNCS 2179, pp. 166-174.
11. G.M. Megson, V.N. Aleksandrov, I.T. Dimov, Systolic Matrix Inversion Using a Monte Carlo Method, Journal of Parallel Algorithms and Applications, Vol. 3, No 3/4, pp. 311-330.
12. A. Owen, Monte Carlo Extension of Quasi-Monte Carlo, in D. J. Medieiros, E. F. Watson, M. Manivannan and J. Carson (eds.), Proceedings of WSC'98, pp. 571-577, 1998.
13. I. M. Sobol, On the distribution of point in a cube and the approximate evaluation of integrals, USSR Computational Mathematics and Mathematical Physics, Vol. 7 (1967) pp. 86-112.
14. J. H. Halton, On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals, Numer. math., Vol. 2 (1960) pp. 84-90.
15. H. Niederreiter, L. Kuipers, Uniform distribution of sequences, John Wiley & sons, New York, 1974.
16. I.M. Sobol, Monte Carlo numerical methods, Nauka, Moscow, 1973.