19.1.5 Newton polynomial

The class  NewtonPolyNomial defines a polynomial described with respect to the Newton basis. We let it inherit some common methods from the polynomial base class, for example, polynomial.plot, polynomial.zeros, and even parts of the __init__ method, by using the command super (see Section 8.5: Subclasses and inheritance):

class NewtonPolynomial(PolyNomial):
    base = 'Newton'
    def __init__(self,**args):
        if 'coeff' in args:
            try:
                self.xi = array(args['xi'])
            except KeyError: 
                raise ValueError('Coefficients need to be given'
                'together with abscissae values xi')
        super(NewtonPolynomial, self).__init__(**args)

Once the interpolation points are given, the computation of the coefficients is performed by:

def point_2_coeff(self):
    return array(list(self.divdiff()))

We used divided differences for computing...