INTERPOLATION ON ARBITRARY REGIONS IN THE COMPLEX-PLANE

A fast and stable numerical algorithm is presented for the interpolati on from an arbitrary Jordan curve in the complex plane to the region b ounded by that curve. The algorithm combines the classical analytical apparatus with the fast multipole method to obtain an order O(N-1.5) p rocedure for the determination of interpolation nodes with N the numbe r of nodes in the discretization of the given curve and order O(M + K) procedure for the actual interpolation from M nodes on the boundary o f the region to K nodes inside the region. The performance of the algo rithm is illustrated with several numerical examples. (C) 1991 Academi c Press.