6.2 Divided Difference Representation of Polynomials

The functions described here manipulate polynomials stored in Newton's divided-difference representation. The use of divided-differences is described in Abramowitz & Stegun sections 25.1.4 and 25.2.26.

Function: int gsl_poly_dd_init (double dd[], const double xa[], const double ya[], size_t size)

This function computes a divided-difference representation of the interpolating polynomial for the points (xa, ya) stored in the arrays xa and ya of length size. On output the divided-differences of (xa,ya) are stored in the array dd, also of length size.

Function: double gsl_poly_dd_eval (const double dd[], const double xa[], const size_t size, const double x)

This function evaluates the polynomial stored in divided-difference form in the arrays dd and xa of length size at the point x. An inline version of this function is used when HAVE_INLINE is defined.

Function: int gsl_poly_dd_taylor (double c[], double xp, const double dd[], const double xa[], size_t size, double w[])

This function converts the divided-difference representation of a polynomial to a Taylor expansion. The divided-difference representation is supplied in the arrays dd and xa of length size. On output the Taylor coefficients of the polynomial expanded about the point xp are stored in the array c also of length size. A workspace of length size must be provided in the array w.