Best approximation in \(L^{\infty}\) via iterative Hilbert space procedures (Q2266195)

In this note it is indicated that the problem of best approximation with respect to the supremum \((L^{\infty})\) norm may be solvable by iterative Hilbert space techniques. The validity of this approach for \(L^ p\), p (even) \(<\infty\), has been established by \textit{L. A. Karlovitz} [ibid. 3, 123-127 (1970; Zbl 0222.41016)]. In the Haar case \((L^{\infty}\) norm) this approach yields a convergent algorithm which is a slight modification of the Remez algorithm.