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Interpolation is the theory of constructing smooth functions, usually polynomials or trigonometric polynomials, whose graph passes through a number of given points in the plane. Splines and Bézier curves, piecewise linear or cubic interpolation, Lagrange and Hermite interpolation are example topics.
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Multivariate polynomial interpolations
The answer to your question highly depends on the domain on which you plan to approximate your function.
For products of compact intervals, e.g. rectangles in the plane, some kind of tensor product c …