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Let $f\colon\mathbb{R}^n\to\mathbb{R}$ be a function. I don't have function definition. It's described as a fuzzy inference system. I have the inference system and can manipulate sample data for each output variable.

I need a polynomial approximation of $f$ (say $g$) having only inputs/outputs of $f$. Such a procedure should be computationally rational and precise enough. For functions defined as $h\colon\mathbb{R}\to\mathbb{R}$ I'm using Beziere curves of degree 4 to approximate polynomial segments and then use normalized B-Spline to calculate Taylor series.

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You are looking for interpolation: Newton polynomial

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