New Root-Seeking Algorithms
04-09-2017, 09:33 PM
Post: #21
 ttw Member Posts: 206 Joined: Jun 2014
RE: New Root-Seeking Algorithms
By happenstance, I came across another (unknown to me) articles on zero-finding. 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 root-finding of non-linear equations to get percentage points of probability curves (the t-distribution and F-distribution mostly).
04-10-2017, 05:01 AM
Post: #22
 Namir Senior Member Posts: 741 Joined: Dec 2013
RE: New Root-Seeking Algorithms
(04-09-2017 09:33 PM)ttw Wrote:  By happenstance, I came across another (unknown to me) articles on zero-finding. 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 root-finding of non-linear equations to get percentage points of probability curves (the t-distribution and F-distribution mostly).

Thanks for the PDF. Kahan articles are always welcome!!
04-13-2017, 01:23 PM
Post: #23
 Namir Senior Member Posts: 741 Joined: Dec 2013
RE: New Root-Seeking 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'
04-15-2017, 10:58 PM
Post: #24
 Namir Senior Member Posts: 741 Joined: Dec 2013
RE: New Root-Seeking 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.

Enjoy!

Namir
04-16-2017, 01:06 PM (This post was last modified: 04-16-2017 01:07 PM by Namir.)
Post: #25
 Namir Senior Member Posts: 741 Joined: Dec 2013
RE: New Root-Seeking 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 pdf-comment 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
04-20-2017, 05:05 AM
Post: #26
 ttw Member Posts: 206 Joined: Jun 2014
RE: New Root-Seeking 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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