Mastering Python for Finance - Second Edition

Combing root-finding methods

It is perfectly possible to write your own root-finding algorithms using a combination of the previously-mentioned root-finding methods. For example, you may use the following implementation:

1. Use the faster secant method to converge the problem to a pre-specified error-tolerance value or a maximum number of iterations
2. Once a pre-specified tolerance level is reached, switch to using the bisection method to converge to the root by halving the search interval with each iteration until the root is found

Brent's method or the Wijngaarden-Dekker-Brent method combines the bisection root-finding method, secant method, and inverse quadratic interpolation. The algorithm attempts to use either the secant method or inverse ...