Fast computation of divided differences and parallel hermite interpolation

We present parallel algorithms for fast polynomial interpolation. These algorithms can be used for constructing and evaluating polynomials interpolating the function values and its derivatives of arbitrary order (Hermite interpolation). For interpolation, the parallel arithmetic complexity is 0(log2 M + log N) for large M and N, where M 1 is the order of the highest derivative information and N is the number of distinct points used. Unlike alternate approaches which use the Lagrange representation, the algorithms described in this paper are based on the fast parallel evaluation of a closed formula for the generalized divided differences. Applications to the solution of dual Vandermonde and confluent Vandermonde systems are described. This work extends previous results in polynomial interpolation and improves the parallel time complexity of existing algorithms. B 1989