Near minimax polynomial approximation (Q1387529)

Let \(f\in C^{n+1} [-1,1]\) and \(p\in P_n\) be the best approximation on \([-1,1]\) to \(f\). A near minimax approximation to \(f\in C^{n+1} [-1,1]\) is a polynomial \(p\in P_n\) satisfying \[ \| f-p\|= {1\over 2^n (n+1)!} \bigl | f(n+1) (\xi)\bigr |, \] where \(\xi\in(-1,1)\) and \(\| \cdot \|\) denotes the Chebyshev norm. In this paper the author gives a representation for linear projection and shows that the near approximation problem is equivalent to a problem of the best approximation of bivariate functions.