The “Combining Coefficient” for Anisotropic Sparse Grids
نویسنده
چکیده
The anisotropic sparse grid is a natural extension of the isotropic sparse grid, adapted for situations in which the behavior of the data varies with respect to particular spatial dimensions. An appropriately configured anisotropic sparse grid can achieve accuracy comparable to that of an isotropic sparse grid, while further compounding the reduction in the number of function evaluations that an isotropic sparse grid offers compared to a product rule. To modify an isotropic sparse grid algorithm into an anisotropic one requires changes to the selection criterion and the combining coefficients used in connection with the component product rules. This article discusses these changes and their implementation in a particular computer code.
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