Optimization of the quasi-Monte Carlo algorithm for solving systems of linear algebraic equations

Vestnik St. Petersburg University, Mathematics - Tập 41 Số 1 - Trang 60-64 - 2008
A. I. Rukavishnikova

Tóm tắt

Từ khóa


Tài liệu tham khảo

S. M. Ermakov, The Monte Carlo Method and Related Problems (Nauka, Moscow, 1975; VEB Deutscher Verlag der Wissenschaften, Berlin, 1975).

J. H. Halton, “Quasi-Probability: Why Quasi-Monte-Carlo Methods are Statistically Valid and How Their Errors can be Estimated Statistically,” Monte Carlo Methods and Applications 11, 203–350 (Walter de Gruyter, 2005).

I. M. Sobol’, Multi-Dimensional Cubature Formulas and Haar Functions (Nauka, Moscow, 1969).

H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods (SIAM, Philadelphia, 1992).

S. M. Ermakov and A. I. Rukavishnikova, “Quasi-Monte Carlo Algorithms for Solving Linear Algebraic Equations,” Monte Carlo Methods and Appl. 12(5), 363–384 (2006).

S. M. Ermakov and W. Wagner, “Monte Carlo Difference Schemes for the Wave Equation,” Monte Carlo Methods and Appl. 8(1), 1–29 (2002).

S.M. Ermakov, “Addendum to a Paper on the Monte Carlo Method,” Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki 41(6), 991–992 (2001) [Computational Mathematics and Mathematical Physics 41 (6), 940 (2001)].

D. L. Danilov, S. M. Ermakov, and J. H. Halton, “Asymptotic Complexity of Monte Carlo Methods for Solving Linear Systems,” J. Statistical Planning and Inference 85(1–2), 5–18 (2000).