Variant of the Secant Method

[Namir]

I implemented the Generalized Secant algorithm in Excel VBA. I used the same order as in the article's example (divided differences for first and second derivatives). The algorithm did better than Newton's method in most cases. The Generalized Secant algorithm needs two initial guesses, while Newton's method needs one. It made a difference in some test if I gave Newton's method the second guess OR averaged the two guesses. The closer of these two values to the neighboring root gave better results.

The algorithm is very interesting!!!

Thanks!

Namir