New Monte Carlo methods with estimating derivatives

著者

• Mikhaĭlov, G. A. (Gennadiĭ Alekseevich)

書誌事項

New Monte Carlo methods with estimating derivatives

G.A. Mikhailov

VSP, 1995

注記

Includes bibliographical references (p. [183]-186)

内容説明・目次

内容説明

01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information. 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.

目次

ESTIMATION OF INTEGRALS AND SOLUTION OF INTEGRAL EQUATIONS Estimation of integrals Recurrent estimates of Monte Carlo method for the solution to an integral equation of the second kind Variance of the basic unbiased estimate Branching chains and solutions to nonlinear equations Cost of various algorithms or solving integral equations Solving problems with stochastic parameters ESTIMATION OF DERIVATIVES Vector Monte Carlo algorithms Calculation derivatives and perturbations with respect to parameters Calculation of parametric derivatives in a special case SOLUTION OF THE HELMHOLTZ EQUATION The 'walk on spheres' process The use of probabilistic representation The use of integral representations New algorithms for variable c(r) 'Walk on spheres' algorithms for solving Helmholtz equation in the n-dimensional space Solving difference equations by the Monte Carlo method Additional remarks SOLUTION OF METAHARMONIC EQUATIONS AND ELLIPTIC SYSTEMS Solution of metaharmonic equations by calculating the parametric derivatives Solving metaharmonic equations of the form p+1u+cu=(-1)p+1g Two-dimensional case Calculation of the covariance function of the solution to the biharmonic equation Monte Carlo solution of Dirichlet problem for elliptic systems with variable parameters MONTE CARLO METHODS WITH CALCULATING PARAMETRIC DERIVATIVES IN THE RADIATION TRANSPORT THEORY Monovelocity transfer process Calculations of derivatives and perturbations Multivelocity radiation transport process with fission Calculation the derivatives with respect to cross-sections Calculating critical values of the parameters: the critical density, the time constant of particle multiplication, the effective multiplication factor Numerical examples Monte Carlo calculations of critical systems with equalization of generations Solving some inverse and stochastic problems of the transfer theory The 'free-path' estimate for solving the transfer equation in total SOLUTION OF NONLINEAR INTEGRAL EQUATIONS Solution of nonlinear integral equations Solution of Dirichlet problem for elliptic equations Minimization of cost of Monte Carlo methods in iterative solution of nonlinear problems Iterative solution of a model kinetic equation Appendix: Some simulation algorithms Numerical simulation of random variables Numerical simulation of random fields Remarks about simulation algorithms with the use of multiprocessor systems References \ authors

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詳細情報

• NII書誌ID(NCID): BA25073074
• ISBN:
  • 9067641901
• 出版国コード: ne
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Utrecht
• ページ数/冊数: viii, 186 p.
• 大きさ: 25 cm
• 分類:
  • NDC9 : 417