Quasi-Monte Carlo method for solving Fredholm equations

Sobol I. M. () and Shukhman B. V. ()
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Sobol I. M.: Keldysh Institute of Applied Mathematics, 4, Miusskaya sq., Moscow, 125047, Russia
Shukhman B. V.: retired fromDepartment of Reactor Physics, Atomic Energy of Canada Ltd., Chalk River, ON, Canada

Monte Carlo Methods and Applications, 2019, vol. 25, issue 3, 253-257

Abstract: A Monte Carlo method used for the estimation of convergent von Neumann series solutions of a Fredholm equation of second kind is considered. The sum z(d)⁢(x){z^{(d)}(x)} of d initial terms of the von Neumann series estimating the solution z⁢(x){z(x)} of the equation is represented as a d-dimensional integral over the unit cube Hd{H_{d}}.This note presents three examples calculating z(d)⁢(x){z^{(d)}(x)} for different kernels with norms ∥K∥

Keywords: Monte Carlo methods (MC); quasi-MC; Fredholm equation; von Neumann series; average dimension; Sobol’ sequence (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1515/mcma-2019-2045

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