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Error Estimation and Optimization of the Functional Algorithms of a Random Walk on a Grid Which Are Applied to Solving the Dirichlet Problem for the Helmholtz Equation

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Abstract

We consider the algorithms of a “random walk on a grid” which are applied to global solution of the Dirichlet problem for the Helmholtz equation (the direct and conjugate methods). In the metric space C we construct some upper error bounds and obtain optimal values (in the sense of the error bound) of the parameters of the algorithms (the number of nodes and the sample size).

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Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Russia

    E. V. Shkarupa

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  1. E. V. Shkarupa
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Shkarupa, E.V. Error Estimation and Optimization of the Functional Algorithms of a Random Walk on a Grid Which Are Applied to Solving the Dirichlet Problem for the Helmholtz Equation. Siberian Mathematical Journal 44, 908–925 (2003). https://doi.org/10.1023/A:1025957324404

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  • DOI: https://doi.org/10.1023/A:1025957324404

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