Numerical approximation

Numerical approximation is proposed to deduce the point that is lost in the dataset, Numerical approximation is useful while some data in a dataset is lost.

Interpolation

Interpolation function is a function that $p a sses t h ro ug h a ll$ the sample point.

Mastering numerical analyze is not needed as the SciPy module have provided all the methods you will need to solve problem of this kind.

import numpy as np
from scipy import interpolate

Interpolation are divided into many parts such as linear interpolation and spline interpolation.

# Linear interpolation
f_linear = interpolate.interp1d(x, y)
# B-spline interpolation
tck = interpolate.splrep(x, y)

There are also many other types of interpolations

for kind in ['nearest', 'zero', 'linear', 'quadratic', 'cubic']:
    f = interpolate.interp1d(x, y, kind=kind)

Least squares fitting

Curve fitting is the process of constructing of a curve or mathematical function, that has the best fit to the data points given. The least squares fitting are the most common method for curve fitting.

import numpy as np
from scipy.optimize import leastsq

# f(x) defines the distance between your fitting function with the actual points
def f(p): 
    k, b = p
    return (Y - (k*x + b))

r = leastsq(f, [1, 0]) # the latter param is the initial k and b given
k, b = r[0]