Newton or Secant?

[Namir]

(04-03-2017 12:40 AM)ttw Wrote:  There is another (poorer) method that sometimes is called the secant method but the proper name is Reguli Falsi. In this case, one does not use the last two iterations like the secant method but uses the last two iterations which have different signs.

The Reguli Falsi is a root-bracketing method, which can run into trouble when one one end of the root-bracketing interval converges to the root. I found an interesting article on the Internet an article titled "A family of regula falsi root-finding methods" by Sérgio Galdino. This article shows several remedies for the Reguli-Falsi's problem. Each remedies allows the root-bracketing interval to properly shrink around the root.