LOGARITHMIC DEPTH CIRCUITS FOR HERMITE INTERPOLATION

Abstract

We present a new parallel algorithm for Hermite interpolation. The algorithm can be implemented using arithmetic-boolean circuits of depth logarithmic and size polynomial in the input size. A corresponding Boolean algorithm can be used to compute the coefficients of the Hermite interpolating polynomial from binary representations of evaluation points and derivatives over finite fields and number fields, using a P-uniform family of circuits of depth logarithmic in the input size and of polynomial size.