Incremental search
A crude method of solving a nonlinear function is by doing an incremental search. Using an arbitrarily starting point 
, we can obtain values of 
for every increment of 
. We assume that the values of 
, 
, 
… are going in the same direction as indicated by their sign. Once the sign changes, a solution is deemed as found. Otherwise, the iterative search terminates when it crosses the boundary point 
.
A pictorial example of the root-finder method for iteration is given in the following graph:
An example can be seen from the Python code:
'''
Python code:
Incremental search method
'''
""" An incremental search algorithm """
import numpy as np
def incremental_search(f, a, b, dx):
"""
:param f: The function to solve
:param a: The left boundary x-axis value
:param b: The right boundary x-axis value
:param dx: The incremental value in searching
:return: The x-axis value of the root,
number of iterations used
"""
fa = f(a)
c...
