Piecewise Multilinear Sparse Grid Interpolation in MATLAB

To recover/approximate smooth multivariate functions, sparse grids are superior to full grids due to a significant reduction of the required support nodes. The order of the convergence rate in the maximum norm is hereby preserved up to a logarithmic factor. We describe three possible piecewise multilinear interpolation schemes in detail and conduct a numerical comparison. Furthermore, we summarize the features of our efficient and easy-to-use sparse grid interpolation software package spinterp for Matlab, which is available for free.

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