The barycentric interpolation algorithm allows easy updating by
adding more points for the polynomial to pass through.
xi : array-like of length N1
The x coordinates of the points the polynomial should pass through
yi : array-like N1 by R or None
The y coordinates of the points the polynomial should pass through;
if R>1 the polynomial is vector-valued. If None the y values
will be supplied later. The yi should be specified if and only if
the interpolator has y values specified.