Error analysis of an adaptive Monte Carlo method for numerical integration

Mathematics and Computers in Simulation

Volumn 47, Issue 2-5, 1998, Pages 201-213

  Karaivanova, Aneta ^a   Dimov, Ivan ^a  

^a BULGARIAN ACADEMY OF SCIENCES   (Bulgaria)

Author keywords

Important sampling; Monte Carlo method; Multidimensional integrals; Superconvergence

Indexed keywords

EID: 0004117047     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-4754(98)00103-7     Document Type: Article

References (16)

1. I.M. Sobol, Monte Carlo Numerical Methods, Nauka, Moscow, 1973.
2. I. Dimov, O. Tonev, Monte Carlo algorithms: performance analysis for some computer architectures, J. Comput. Appl. Math. 48 (1993) 253-277.
3. S. Haber, A modified Monte Carlo quadrature, Math. Comput. 20(95) (1966) 361-368; 21(99) (1967) 388-397.
4. S. Haber, A modified Monte Carlo quadrature, Math. Comput. 20(95) (1966) 361-368; 21(99) (1967) 388-397.
5. S.M. Nikolski, Quadrature formulas, Nauka, Moscow, 1988.
6. n, Part 2, Handbook of Numerical Analysis, vol. 3, North-Holland, Amsterdam, 1994.
7. N.S Bahvalov, On the optimal estimations of convergence of the quadrature processes and integration methods: Numerical methods for solving differential and integral equations, Nauka, Moscow, 1964, pp. 5-63.
8. I. Dimov, O. Tonev, Monte Carlo methods with overconvergent probable error, in: Proceedings of the International Conference on Numerical Methods and Application, Sofia, Bulgarian Academy of Sciences, Sofia, 1989, pp. 116-120.
9. V. Dupach, Stochasticke pocetni metody, Cas. pro pest. mat. 81(1) (1956) 55-68.
10. Bl. Sendov, V. Popov, Averaged moduli of smoothness, Mir, Moscow, 1988.
11. M.D. Takev, On Probable Error of the Monte Carlo Method for Numerical Integration, Math. Balkanica (New Series) 6 (1992) 231-235.
12. H. Kahn, Random sampling (Monte Carlo) techiques in neutron attenuation problems, Nucleonics 6(5) (1950) 27-33; 6(6) (1950) 60-65.
13. H. Kahn, Random sampling (Monte Carlo) techiques in neutron attenuation problems, Nucleonics 6(5) (1950) 27-33; 6(6) (1950) 60-65.
14. G.A. Mikhailov, Optimization of the "weight" Monte Carlo methods, Moscow, 1987.
15. I.T. Dimov, Minimization of the probable error for some Monte Carlo methods, in: Andreev, Dimov, Markov, Ullrich (Eds.), Mathematical Modelling and Scientific Computations, Bulgarian Academy of Sciences, Sofia, 1991, pp. 159-170.
16. Davis, Rabinowitz, Methods of Numerical Integration, Academic Press, NY, 1984.