7.7 Hybrid Methods
This section is devoted to hybrid or “omnibus” algorithms, whereby two or more methods are combined into one process. There are several sub-categories of such combined methods dealt with in the literature, such as bisection-secant, bisection-secant-quadratic (or cubic), bisection-Newton, bisection-Steffensen-like, and a few others. Most of them involve bracketing and apply only to real roots (but a few deal with complex roots). We will discuss the above-mentioned categories in the above order, which happens to be roughly chronological as well.