On Convergence Rates of Root-Seeking Methods
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01-31-2017, 06:20 AM
Post: #3
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RE: On Convergence Rates of Root-Seeking Methods
(01-30-2017 10:06 PM)emece67 Wrote: Thanks a lot, Namir, for your work. Excellent comments and very good explanation. I learned a few interesting things of the study I did. First, the approximations that I used for the derivative, slowed the convergence to some extent. Second, I often use initial guesses that do not share any digits with the actual roots. You explain very well how that affects convergence. Third lesson learned is that the function, its roots, proximity of the roots from each other, changes in the slope (first derivative) values, and changes in the curvature (second derivative) values are all factors that greatly influence convergence rates. Add to all that the proverbial monkey wrench of fundamental problems with reaching the root (extended range of x near the root where the first derivative is near zero, or parallel function asymptotes around the root, that cause refined guess values to cycle). Finding test functions used to calculate convergence rates and yield good results is not a trivial process. Namir |
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