I have been working on a pair of similar root-seeking algorithms in the past few weeks. I finished writing an article (click here) that describes the algorithms (which I name the Probing Slopes Algorithms and Probing Steps Algorithm) and compares them with Newton's method. My article also includes three test functions used to compare the new algorithms with Newton's method, using Excel VBA. I am excited to report that the new algorithms find the root in fewer loops and also make fewer function calls than Newton's method.

Namir

**PS: Based on the feedback of kind folks on this web site, you will need to use FireFox to view the article's text AND figures. some how, Microsoft IE does not show the images.**

*Edited: 8 Nov 2007, 12:36 p.m. after one or more responses were posted*