Nevilles Method

Newton's method of interpolation involves two steps computation of the coefficients, followed by evaluation of the polynomial. This works well if the interpolation is carried out repeatedly at different values of x using the same polynomial. If only one point is to be interpolated, a method that computes the interpolant in a single step, such as Neville's algorithm, is a better choice. Let Pk x, xi 1, , xi k denote the polynomial of degree k that passes through the k 1 data points x,, yi , xi...