Complex Rational Approximation by Interpolation at Preselected Nodes.

摘要

Let omega be a finitely connected closed point set in the complex plane with a piecewise smooth boundary. The approximation of functions analytic on omega by rational functions determined by interpolation or least squares approximation at preselected nodes is discussed. Attention is focussed on simple methods for selecting an appropriate rational space and obtaining a fairly well-conditioned rational basis. Applications include the determination of conformal mappings. Numerical examples illustrate the approximation method. (Author)