maths.numerical_analysis.nevilles_method

Python program to show how to interpolate and evaluate a polynomial using Neville’s method. Neville’s method evaluates a polynomial that passes through a given set of x and y points for a particular x value (x0) using the Newton polynomial form. Reference:

Functions

neville_interpolate(→ list)

Interpolate and evaluate a polynomial using Neville's method.

Module Contents

maths.numerical_analysis.nevilles_method.neville_interpolate(x_points: list, y_points: list, x0: int) → list

Interpolate and evaluate a polynomial using Neville’s method. Arguments:

x_points, y_points: Iterables of x and corresponding y points through

which the polynomial passes.

x0: The value of x to evaluate the polynomial for.

Return Value: A list of the approximated value and the Neville iterations

table respectively.

>>> import pprint
>>> neville_interpolate((1,2,3,4,6), (6,7,8,9,11), 5)[0]
10.0
>>> pprint.pprint(neville_interpolate((1,2,3,4,6), (6,7,8,9,11), 99)[1])
[[0, 6, 0, 0, 0],
 [0, 7, 0, 0, 0],
 [0, 8, 104.0, 0, 0],
 [0, 9, 104.0, 104.0, 0],
 [0, 11, 104.0, 104.0, 104.0]]
>>> neville_interpolate((1,2,3,4,6), (6,7,8,9,11), 99)[0]
104.0
>>> neville_interpolate((1,2,3,4,6), (6,7,8,9,11), '')
Traceback (most recent call last):
    ...
TypeError: unsupported operand type(s) for -: 'str' and 'int'