An implementation, based on iterative techniques, of a method to compute the Riemann mapping function is presented. The method has been recently introduced by N. Kerzman and the author; it expresses the Szego kernel as the solution of an integral equation of the second kind. It is shown how to treat symmetric regions. The algorithm is tested on five examples. The numerical results show that the method is competitive, with respect to accuracy, stability, and efficiency.
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