On Convergence Rates of Root-Seeking Methods

[Paul Dale]

(03-12-2018 04:13 PM)Claudio L. Wrote:  Brent seems like a powerhouse combo of other methods. If I implement Brent, does it make any sense to offer the user a choice to use bisection, etc.?

I don't think bisection would make sense, Brent has the same guaranteed convergence if the root is bracketed. Newton's might, especially if you pass in the function and its derivative.

The GNU Scientific Library provides six methods, three bracket based and three derivative based. They include Steffenson's method which requires the derivative but which converges faster than Newton's. Interestingly, no higher order methods are included.

Quote:It will probably end up being the default method, unless complex mode is enabled, then something like Muller seems to be the only choice?

The GNU Scientific Library provides two methods, one using derivative and one without. I've not looked into this, so can't comment further.


Pauli