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New Monte Carlo Methods With Estimating Derivatives
Gennadij A. Michajlov
出版VSP, 1995-01-01
主題Science / Physics / Mathematical & ComputationalArchitecture / Interior Design / GeneralScience / General
ISBN97890676419069067641901
URLhttp://books.google.com.hk/books?id=kFtL4XL9HtUC&hl=&source=gbs_api
EBookSAMPLE
註釋It is possible to use weighted Monte Carlo methods for solving many problems of mathematical physics (boundary value problems for elliptic equations, the Boltzmann equation, radiation transfer and diffusion equations). Weight estimates make it possible to evaluate special functionals, for example, derivatives with respect to parameters of a problem.
In this book new weak conditions are presented under which the corresponding vector Monte Carlo estimates are unbiased and their variances are finite. The author has also constructed new Monte Carlo methods for solving the Helmholz equation with a nonconstant parameter, including the stationary Schrodinger equation. New results for linear and nonlinear problems are also presented. Some methods of random function simulation are considered in the special appendix. A new method of substantiating and optimizing the reccurent Monte Carlo estimates without using the Neumann series is presented in the introduction.