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In this paper we consider an orthonormal basis, generated by a tensor productof Fourier basis functions, half period cosine basis functions, and theChebyshev basis functions. We deal with the approximation problem in highdimensions related to this basis and design a fast algorithm to multiply withthe underlying matrix, consisting of rows of the non-equidistant Fouriermatrix, the non-equidistant cosine matrix and the non-equidistant Chebyshevmatrix, and its transposed. This leads us to an ANOVA (analysis of variance)decomposition for functions with partially periodic boundary conditions throughusing the Fourier basis in some dimensions and the half period cosine basis orthe Chebyshev basis in others. We consider sensitivity analysis in thissetting, in order to find an adapted basis for the underlying approximationproblem. More precisely, we find the underlying index set of themultidimensional series expansion. Additionally, we test this ANOVAapproximation with mixed basis at numerical experiments, and refer to theadvantage of interpretable results.

ANOVA approximation with mixed tensor product basis on scattered points