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Quasi-Monte Carlo method for solving Fredholm equations

Author

Listed:
  • 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)

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∥

Suggested Citation

  • Sobol I. M. & Shukhman B. V., 2019. "Quasi-Monte Carlo method for solving Fredholm equations," Monte Carlo Methods and Applications, De Gruyter, vol. 25(3), pages 253-257, September.
    • Handle: RePEc:bpj:mcmeap:v:25:y:2019:i:3:p:253-257:n:6
    DOI: 10.1515/mcma-2019-2045
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    References listed on IDEAS

    as
    1. Liu, Ruixue & Owen, Art B., 2006. "Estimating Mean Dimensionality of Analysis of Variance Decompositions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 712-721, June.
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    Cited by:

    1. Sobol Ilya M. & Shukhman Boris V., 2020. "QMC integration errors and quasi-asymptotics," Monte Carlo Methods and Applications, De Gruyter, vol. 26(3), pages 171-176, September.

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