Degree reduction of Bézier curves and filter banks (Q1921228)

The paper is on degree reduction of a given Bézier function (i.e., a polynomial) \(f^n\) of degree \(n\). That is, one has to find a polynomial \(f^{n-1}\) such that \(|e^n|:= |f^n-f^{n-1}|\) is minimal. The authors obtain a general solution for this problem, and apply it to the case of the \(L_1\)-, \(L_2\)- and the \(L_\infty\)-norm, where results in terms of the Legendre resp. Chebyshev polynomials are recovered.