Numerical Methods for Roots of Polynomials - Part II

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.

The first hybrid algorithm seems to have been “put together” by Wijngaarden et al (1963) and Wilkinson (1967). It was first published in an accessible journal by Peters and Wilkinson ...