A few threads back Hugh Steers pointed out a method for finding the roots of a nonlinear function by Russian mathematician Ostrowski. I checked Luyka's web page which discussed that method and presented the code for the algorithm. It did real well.

I further searched the Internet for articles about root-seeking method based on Ostrowski's method. I found several articles that further accelerated the convergence for that algorithm. A few articles were published by Chinese mathematician Zou (and colleagues) and offer somewhat elaborate enhancements to Ostrowski's method. These enhancements can solve for a root in TWO iterations (requiring 9 function calls) as compared to 6 iterations (and 12 function call) with Newton's method!. The fast Halley's method required 3 iterations and 9 function calls. The basic Ostrowski method took 3 iterations and 7 function call.

So thank you Lyuka for pointing me to Ostrowski's method. I really enjoyed learning about it and about its variants.

More gems in the root-seeking toolbox. Just when I thoght I learned about all the algorithms available, I get to learn about new and even more efficient ones!!

Namir