New RootSeeking Algorithms

04092017, 09:33 PM
Post: #21




RE: New RootSeeking Algorithms
By happenstance, I came across another (unknown to me) articles on zerofinding. One is a bunch of notes by Bill Kahan.
https://people.eecs.berkeley.edu/~wkahan...lRoots.pdf I'll probably implement something like the Illinois algorithm with a double speed secant method. I've been using rootfinding of nonlinear equations to get percentage points of probability curves (the tdistribution and Fdistribution mostly). 

04102017, 05:01 AM
Post: #22




RE: New RootSeeking Algorithms
(04092017 09:33 PM)ttw Wrote: By happenstance, I came across another (unknown to me) articles on zerofinding. One is a bunch of notes by Bill Kahan. Thanks for the PDF. Kahan articles are always welcome!! 

04132017, 01:23 PM
Post: #23




RE: New RootSeeking Algorithms
I am currently working on the set of modified Newton's methods mentioned in the links given in an earlier message in this thread, plus other similar methods that I stumbled upon the web. So far I have about 39 methods and their variants. Some algorithms give regular equations while others give families of equations.
When I am done, I will publish the Excel file on my web site. The VBA code contains references to the articles (which I plan to also include in a ZIP file), I will include a Word doc file that will contain a very short comment on the various algorithms. Namir Still truckin' 

04152017, 10:58 PM
Post: #24




RE: New RootSeeking Algorithms
Hello All,
I have posted on my web site a ZIP file that contains the following: 1) An Excel file that tests about 59 algorithms (and variants) for modified Newton's method. The file has several worksheets to test various functions (some with different initial guesses) and accessible VBA code that shows the implementation for the various modified Newton methods. 2) A PDF that contains a short summary for the results. 3) A set of PDF file containing the articles I used to obtain the equations used in various modified Newton methods. To download the ZIP file click here. Enjoy! Namir 

04162017, 01:06 PM
(This post was last modified: 04162017 01:07 PM by Namir.)
Post: #25




RE: New RootSeeking Algorithms
I rearranged the contents of the ZIP file that you can download in my last message. I created a subfolder for the articles and left my pdfcomment file and the main Excel file in the default ZIP root folder. This new arrangement will make it effortless to spot the pdf that contains my brief comments on the results.
Namir 

04202017, 05:05 AM
Post: #26




RE: New RootSeeking Algorithms
http://www.math.cornell.edu/~hubbard/New...tiones.pdf
How To Find All Roots of Complex Polynomials by Newton's Method Used the dynamics of Newton's method from differing starting points to guarantee convergence to each root. 

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