Worse than Bisection???!!!!

01262014, 02:36 PM
(This post was last modified: 01262014 02:37 PM by Namir.)
Post: #1




Worse than Bisection???!!!!
I thought that the Bisection method was the slowest rootseeking method for nonlinear functions. I set out, for the pure fun of it, to write an algorithm that can actually do worse!!! The proposed method starts at a point X and marches (in positive or negative steps) towards the targeted root. When the method detects that the function at the current value of X has changed sign, it switched the sign of the step value and reduces it by 2. Thus, the method (which I call Dancer) dances around the root until the search step falls below a tolerance value. The method is very much influenced by how close you choose the initial X to the root and by the initial step size. I did contemplate substeps to accelerate the march towards the root, but I was concerned that I would create problems when the nonlinear function has multiple roots that lie close to each other.
Here is the pseudocode: Code: Give starting value X, Step dx, and tolerance value toler: I implemented the above algorithm in Excel VBA, along with code for the Bisection method. The latter method did much better in all of the tests I conducted. The Dancer method took 30% to 100% more iterations to get the answer!! Please no hate mail for this mediocre method. :) 

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Messages In This Thread 
Worse than Bisection???!!!!  Namir  01262014 02:36 PM
RE: Worse than Bisection???!!!!  Thomas Klemm  01262014, 06:01 PM
RE: Worse than Bisection???!!!!  Namir  01262014, 07:06 PM
RE: Worse than Bisection???!!!!  Thomas Klemm  01262014, 10:53 PM
RE: Worse than Bisection???!!!!  Dan W  01282014, 03:18 AM
RE: Worse than Bisection???!!!!  ttw  07172014, 06:38 PM
RE: Worse than Bisection???!!!!  Namir  07172014, 08:43 PM

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