Mathematical Sciences 428

This paper describes a fast and reliable algorithm which computes smooth piecewise polynomial approximations to functions. It adaptively locates the knots by a procedure that has been shown to provide the optimal rate of convergence as the accuracy requirements (and number of knots) increase. Local Hermite interpolation is used which requires that derivatives of the function be known (or estimated accurately) and that the polynomial degree plus one be twice the smoothness. The theoretical background and interesting algorithm components are described briefly then algorithm usage (user interface, role of two unusual arguments, portability) are discussed in more detail. A very brief summary is given of the extensive testing performed. The algorithm is first described in a very high level language (about 120 lines) and then given in Fortran (about 1250 lines). A test driver and a FUNCTION subprogram containing 20 fun~tio~s (with derivatives) are also given which are useful for testing this and other similar algorithms