Abstract
Given a polynomial p of degree n we want to find a best L 2 -approximation over the unit interval from polynomials of degree m<n. This problem is shown to be equivalent to the problem of finding the best Euclidean approximation of the vector of Bernstein–Bézier coefficients of p from the vector of degree-raised Bernstein–Bézier coefficients of polynomials of degree m.
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