An algorithm for Chebyshev approximation by rationals with constrained denominators
Let \(B\) be a compact Hausdorff space, and let \(C(B)\) be the space of all continuous real-valued functions on \(B\). Further it is assumed that: (i) \(\mu\) and \(\nu\) are fixed elements of \(C(B)\) such that \(0<\mu\leq\nu\); (ii) \(Z\) is a nonempty closed subset of \(\mathbb{R}^n\); (iii) \(V\) and \(W\) are continuous maps of \(\mathbb{R}^n\) into \(C(B)\); (iv) \({\mathcal H}\) is a continuous map of \(C(B)\times C(B)\) into \(C(B)\). Based on these data the author proposes a modified differential correction algorithm for determining the value \(\inf_{z\in F} \sup_{t\in B}f(z)(t)\), where \(F:= \{z\in\mathbb{Z}: \mu\leq W(z)\leq\nu\}\) and \(f(z):= {\mathcal H}(V(z),W(z))/ W(z)\). The discussion of this algorithm is completed by convergence results and numerical examples. Finally, it should be mentioned that the algorithm described in the present paper has some advantages in comparison with the original differential correction algorithm.
scientific article; zbMATH DE number 922394