On Convergence Rates of Root-Seeking Methods

[Claudio L.]

(03-12-2018 11:18 PM)Paul Dale Wrote:  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.

Thanks for the feedback. If GSL provides Brent, bisection and regula falsi, I should probably provide at least those 3 to the user. Even if it doesn't make sense, just for fun.
For non-bracketed ones, secant, Newton and Steffensen (I need to research this one, first time I hear its name), seems fairly vanilla. Perhaps I'll add some of Namir's experiments with Ostrowski, Halley, etc. just to keep it interesting.

(03-12-2018 11:18 PM)Paul Dale Wrote:  The GNU Scientific Library provides two methods, one using derivative and one without. I've not looked into this, so can't comment further.

I couldn't find any reference to this in the GSL docs (?)

Pauli
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