The HP 48 object listed below in ->ASC form is a high-performance polynomial root finder. Those of you who remember the HP 71B Math Pac will recognize this as the same as the PROOT command from that Pac; it is in fact the same assembly-language code, given an RPL front end to operate in the HP 48.
Found on https://www.hpmuseum.org/forum/thread-10967-post-160700.html#pid160700
See also http://www.jeffcalc.hp41.eu/emu71/mathrom.html#src for the uncommented source code of PROOT and other functions of the HP71B math pack.

Apart from the blog, there are technical notes https://www.johndcook.com/blog/writing/ and on-line calculators https://www.johndcook.com/blog/online-calculators/
As an example, see Camp-Paulson normal approximation to the binomial distribution https://www.johndcook.com/blog/camp_paulson/
The articles https://www.johndcook.com/blog/2024/04/01/more-laguerre-images/ and
https://www.johndcook.com/blog/2024/03/22/laguerres-root-finding-method/ demonstrate the basins of attraction for Laguerre's root-finding method.
https://www.johndcook.com/blog/2018/11/24/spheroid-distance/ should be useful for azel.
https://www.johndcook.com/blog/2020/02/08/arenstorf-orbit/ shows a periodic solution to the restricted 3-body problem.
https://www.johndcook.com/blog/2022/11/14/simultaneous-root-finding/ describes the Durand-Kerner polynomial root finding method.
https://www.johndcook.com/blog/2022/11/01/kepler-newton/ discusses solving Kepler's equation

TODO: https://www.johndcook.com/blog/2022/10/30/arctan-k-tan-t/ states "This plot looks similar to the plot of true anomaly for a highly elliptical orbit. I’m sure they’re related, but I haven’t worked out exactly how."

https://www.johndcook.com/blog/2022/10/21/math-origins/ explains V.I. Arnolds comment
"All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like), hydrodynamics (supported by manufacturers of atomic submarines), and celestial mechanics (financed by military and other institutions dealing with missiles, such as NASA)."

https://www.johndcook.com/blog/2018/09/24/riemann-hypothesis-the-fine-structure-constant-and-the-todd-function/ is about  Sir Michael Atiyah's incorrect proof of Riemann's hypothesis, the article https://rjlipton.com/2018/09/26/reading-into-atiyahs-proof/ is an interesting read. (I had bookmarked this entry on Wed Sep 26 15:51:47 2018 and put it here 2024-04-03.)

The article https://www.johndcook.com/non_central_chi_square.pdf sounds interesting:
John D. Cook Upper bounds on non-central chi-squared tails and truncated normal moments (2010). UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series. Working Paper 62.
Abstract. We show that moments of the truncated normal distribution provide upper bounds on the tails of the non-central chi-squared distribution, then develop upper bounds for the former.

Citation of Brian Smith's work on the ZPOLY root-finding algorithm.
On 2022-07-25, the link points to the IMSL Numerical Libraries page. Does not matter, because I have found the document via http://portal.acm.org/citation.cfm?id=321615&dl=GUIDE&coll=&CFID=15151515&CFTOKEN=6184618 /add source/