Hermite interpolation in python with out using scipy library

Question

def hermite_interpolation(x, y, yp, xi):
    n = len(x) - 1
    result = 0.0

    for j in range(n + 1):
        term = y[j]
        for i in range(n + 1):
            if i != j and x[j] != x[i]:
                term *= (xi - x[i]) / (x[j] - x[i])
        result += term * (1 + 2 * (xi - x[j]) / (x[j] - x[i])) * (xi - x[j]) ** 2

    return result

error:

divide by zero encountered in scalar divide result += term * (1 + 2 * (xi - x[j]) / (x[j] - x[i] )) * (xi - x[j])**2

the function i want to interpolate is y = 1 / (x**2 + 1) in the interval of [0,1] for equal spaced point. i tried to add epsilon to it but the the interpolation error increased significantly what shall i do?

Answer 1

You'll need to change the method. One possible search term is osculatory interpolation.