Adaptive Simpson and Romberg integration methods

[robve]

(03-25-2021 11:57 PM)Valentin Albillo Wrote:  Note: In everything that follows, no offence is ever meant, it's just my trademark style when I feel skeptic (let's say) about some statement or other, in particular if not supported by facts. IMHO, of course.

No offense. As I told my former students, critical thinking is important and do not stop questioning, but use the answers to analyze ideas and adjust them accordingly. We all build on existing work published by others and give credit for their efforts.

I am not sure what to think of statements like that and the references to "my method", which I never have used. I noticed that "your method" pzer on the HP-71B in every detail implements the standard Weierstrass / Durand-Kerner method for polynomial complex root finding aka "root polishing". I easily spotted this, because of the way you've set up the initial roots and the root polishing. Yet, nowhere is Durand-Kerner mentioned in your article. Further, it is the most bare and simple implementation.

There is actually more we can do beyond the basics, such as 1) removing trailing (in the code, leading in the poly) zero coefficients before polishing the roots, since these do not contribute to the result; 2) reject insignificant nonzero real or imaginary parts in the roots finally found. These require a little bit of code and incur almost no overhead. These additions are quite easy and often found in implementations.

So no offense as my post is derived from public existing work anyway, just like yours is.

- Rob