New Root-Seeking Algorithms

[ttw]

Another possibility is to use variable step lengths. I don't have a quick rule of thumb, but there are some in the various references. The idea is to automatically adjust step length as the computation proceeds. This is often with the Levenberg-Marquardt method for multidimensional problems.

If error estimation is easy, one just increases the step length until things don't work then backs off. (There are good discussions on the Wiki for the Nelder-Mead Creeping Simplex optimization method.) I used to lengthen by 3 and shrink by 2 as the actual numbers don't matter; one eventually gets 3^n/2^m with n stretches and m shrinks.

I also found a new reference: http://citeseerx.ist.psu.edu/viewdoc/dow...1&type=pdf