Mastering Python for Finance - Second Edition

Incremental search

A crude method of solving a nonlinear function is by doing an incremental search. Using an arbitrary starting point, a, we can obtain values of f(a) for every increment of dx. We assume that the values of f(a+dx), f(a+2dx), f(a+3dx)… 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, b.

A pictorial example of the root-finder method for iteration is given in the following graph:

An example can be seen from the following Python code:

In [ ]:    """     An incremental search algorithm  """ ...