[VA] SRC #012b - Then and Now: Root

[J-F Garnier]

(11-12-2022 05:21 AM)C.Ret Wrote:  Still have a question, I notice that all the roots found by PROOT are within the unit circle centered at the origin of the complex plane.
Is there any reason for that?

I believe for the same reason I indicated in my first post above:

(11-09-2022 08:43 AM)J-F Garnier Wrote:  My first thoughts: a real root must be negative, and greater than -1 since the polynomial quickly takes very large values for |X|>1.

Transposed for complex roots, it means the roots must be |z|<1.
And I believe this is also related to this comment of Valentin:

(11-12-2022 12:59 AM)Valentin Albillo Wrote:  Finally, I feel that few of you heeded my advice about properly balancing the work done by the program vs. the work done by the programmer, with some of you actually doing a lot of work to then have the program doing the very minimum work necessary, or the other way around.

This is experimental math for most of us, as Valentin recently pointed it out. Fernando and I (and maybe others silently) tried with PROOT and found a candidate for the minimum root, and the fact that it was small enough lead me to my analysis and my solution with 200 terms.

J-F