An Algorithm for General Restricted Rational Chebyshev Approximation

In [R. Hettich and P. Zencke, Teubner Studienbücher Mathematik, Leipzig, Stuttgart, 1982] and [G. Speich, Ph.D. thesis, University of Bonn, Bonn, 1981] a Newton-type differential correction algorithm for general rational Chebyshev approximation has been introduced that has been shown to be globally convergent and superlinearly convergent under assumptions weaker than the common condition of unique solutions. Using recent results on parametric semi-infinite programming [Math. Programming, 38 (1987), pp. 323–340], it can be shown that all essential assumptions can be dropped without destroying superlinear convergence. Moreover, additional constraints on the problem, such as restrictions on the range, can be treated without destroying the favorable properties of the algorithm.