The Sparse Grid Interpolant
نویسنده
چکیده
Smolyak’s sparse grid construction is commonly used in a setting involving quadrature of a function of a multidimensional argument over a product region. However, the method can be applied in a straightforward way to the interpolation problem as well. In this discussion, we outline a procedure that begins with a family of interpolants defined on a family of nested tensor product grids, and demonstrate how the Smolyak rule can be used to generate an interpolant of known precision. We also consider the issues that arise when a family of non-nested tensor product grids are used, such as sequences of Gauss-Legendre quadrature abscissas.
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