Uniform approximation as a numerical tool for constructing conformal maps (Q1072673)

As proposed in earlier papers by \textit{G. Opfer} [Numer. Math. 35, 189-200 (1980; Zbl 0417.30012) and ibid. 39, 411-420 (1982; Zbl 0517.65005)], the problem of finding the conformal mapping \(f_ 0\) of a domain R onto the unit disk D is replaced by an infinite optimization problem, the discretization of which leads to an approximation of \(f_ 0\). A modification yields the map onto a polygon instead of D. The new feature of this paper is the introduction of special functions into the polynomial basis so that a better approximation of \(f_ 0\) is obtained.