On the numerical recovery of a holomorphic mapping from a finite set of approximate values

Summary. The least squares approach for the recovery of a holomorphic mapping from given perturbed nodal values is considered. The mapping is assumed to be a priori bounded by a known quantity, so that the recovery problem is well-posed. The present analysis shows that for nodes that are the zeroes of Jacobi polynomials a quasioptimal algorithm results with a fairly moderate number of nodes. The analysis also takes into account the effect of the numerical linear algebra involved. Some numerical experiments are presented. Received June 10, 1999 / Revised version received July 16, 2001 / Published online September 19, 2001