The differential correction algorithm for rational L∞ approximation

摘要: Given a set of function values f(xt) (t=1,2,...,N), we consider the problem calculating rational R(x)=P(x)/Q(x) that minimizes quantity $$\begin{gathered}\max |f(xt) - R(xt)|, \hfill \\t \\\end{gathered}$$ where P(x) and Q(x) are polynomials prescribed degrees. To solve this Cheney Loeb [2] proposed "differential correction algorithm", ODC say, but in subsequent paper [3] they modified their algorithm, now DC is nearly always used place ODC. The purpose to direct attention back original because practice seems be much better.