Abstract
In this paper we propose a new class of congruential pseudo random number generator based on sequences generating permutations. These sequences have been developed for other applications but our analysis and experiments show that they are appropriate for approximation of multiple integrals and integral equations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Broy, M.: Software engineering — from auxiliary to key technologies. In: Broy, M., Dener, E. (eds.) Software Pioneers, pp. 10–13. Springer, Heidelberg (2002)
Dod, J.: Effective substances. In: The Dictionary of Substances and Their Effects. Royal Society of Chemistry (1999), DIALOG, http://www.rsc.org/dose/titleofsubordinatedocument. (cited January 15, 1999)
Geddes, K.O., Czapor, S.R., Labahn, G.: Algorithms for Computer Algebra. Kluwer, Boston (1992)
Hamburger, C.: Quasimonotonicity, regularity and duality for nonlinear systems of partial differential equations. Ann. Mat. Pura. Appl. 169, 321–354 (1995)
Atanassov, E., Karaivanova, A., Gurov, T., Ivanovska, S., Durchova, M., Dimitrov, D.: Quasi-Monte Carlo integration on the grid for sensevity studies. Earth Sci. Inform. 3, 289–296 (2010)
Blum, M., Micali, S.: How to Generate Cryptographically Strong Sequences of Pseudo-Random Bits. SIAM J. Comput. 13, 850–864 (1984)
Goldreich, O.: Pseudorandomness. Notices 46(10), 1209–1216 (1999)
Gurov, T.V., Dimov, I.T.: A Parallel Monte Carlo Method for Electron Quantum Kinetic Equation. In: Lirkov, I., Margenov, S., Waśniewski, J., Yalamov, P. (eds.) LSSC 2003. LNCS, vol. 2907, pp. 153–161. Springer, Heidelberg (2004)
Kolmogorov, A.: Three approaches to the concept of the amount of information. Probl. Inf. Transm. 1(1), 1–7 (1965)
L’Ecuyer, P.: Uniform random number generation. Annals of Operations Research 53, 77–120 (1994)
L’Ecuyer, P.: Uniform random number generation. In: Henderson, S.G., Nelson, B.L. (eds.) Ch. 3, Simulation, Handbooks in Operations Research and Management Science, pp. 55–81. Elsevier, Amsterdam (2006)
L’Ecuyer, P.: Pseudorandom Number Generators, in Encyclopedia of Quantitative Finance. In: Cont, R. (ed.) Simulation Methods in Financial Engineering, pp. 1431–1437. John Wiley, Chichester (2010)
Li, M., Vitanyi, P.: An Introduction to Kolmogorov Complexity and Its Applications. Springer, New York (1993)
Manev, N.: Sequences generating permutations. Applied Mathematics and Computation 216, 708–718 (2010)
Nedjalkov, M., Gurov, T.V., Kosina, H., Whitlock, P.A.: Statistical Algorithms for Simulation of Electron Quantum Kinetics in Semiconductors - Part II. In: Margenov, S., Waśniewski, J., Yalamov, P. (eds.) LSSC 2001. LNCS, vol. 2179, pp. 183–190. Springer, Heidelberg (2001)
Owen, A.: The dimension distribution and quadrature test functions. Stat. Sin. 13, 1–17 (2003)
Schmid, W., Uhl, A.: Techniques for parallel quasi-Monte Carlo integration with digital sequences and associated problems. Math. Comp. Sim. 55, 249–257 (2001)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag GmbH Berlin Heidelberg
About this paper
Cite this paper
Gurov, T., Ivanovska, S., Karaivanova, A., Manev, N. (2012). Monte Carlo Methods Using New Class of Congruential Generators. In: Kocarev, L. (eds) ICT Innovations 2011. ICT Innovations 2011. Advances in Intelligent and Soft Computing, vol 150. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28664-3_24
Download citation
DOI: https://doi.org/10.1007/978-3-642-28664-3_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28663-6
Online ISBN: 978-3-642-28664-3
eBook Packages: EngineeringEngineering (R0)