Optimization of Weighted Monte Carlo Methods - Hardcover

Mikhailov, Gennadii A.

Hardcover

ISBN 10: 3540530053 ISBN 13: 9783540530053

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1992

Synopsis

The Monte Carlo method is based on the munerical realization of natural or artificial models of the phenomena under considerations. In contrast to classical computing methods the Monte Carlo efficiency depends weakly on the dimen­ sion and geometric details of the problem. The method is used for solving complex problems of the radiation transfer theory, turbulent diffusion, chemi­ cal kinetics, theory of rarefied gases, diffraction of waves on random surfaces, etc. The Monte Carlo method is especially effective when using multi-processor computing systems which allow many independent statistical experiments to be simulated simultaneously. The weighted Monte Carlo estimates are constructed in order to diminish errors and to obtain dependent estimates for the calculated functionals for different values of parameters of the problem, i.e., to improve the functional dependence. In addition, the weighted estimates make it possible to evaluate special functionals, for example, the derivatives with respect to the parameters. There are many works concerned with the development of the weighted estimates. In Chap. 1 we give the necessary information about these works and present a set of illustrations. The rest of the book is devoted to the solution of a series of mathematical problems related to the optimization of the weighted Monte Carlo estimates.

About this title

Synopsis

Weighted Monte Carlo algorithms are useful when direct simulation techniques are inapplicable or ineffective in computer science and technology. This book presents methods which minimize the computer time and memory required in constructing statistical models for systems described by integral equations. Specific topics covered include the optimization of randomized algorithms for estimating probabilistic characteristics of equations with random parameters and applications; computational models for random fields and numerical simulations; vector Monte Carlo algorithms for solving systems of integral equations; and a special approach to the application of perturbation theory based on this method.

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1992
• ISBN 10: 3540530053
• ISBN 13: 9783540530053
• Binding: Hardcover
• Language: English
• Number of pages: 236