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.
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.
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Produkt-Hinweis
Gewicht
ISBN-13
978-90-6764-190-6 (9789067641906)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Klassifikation
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
