Nick Higham

Prof Higham has quite the list of papers on the finer points of numerical algorithms going back to his MSc in 1983:

http://www.ma.man.ac.uk/~higham/papers/bibbase.php

including a brief note on the comparing "Top 10 Algorithms in Applied Mathematics" between 2000 and 2016 that may interest some:

https://nhigham.com/2016/03/29/the-top-10-algorithms-in-applied-mathematics/

It'd be nice to see some meat on the bones and a few ripping yarns about the application end of applied math techniques .. eg: forming an enhanced image from tens (or hundreds) of thousands of multichannel spectral samples using a sensitivity adjusted SVD, and then removing the most common expected background to highlight the anomalies.

It's dry stuff in Linear Algebra, somewhat more exciting when searching for nuclear weapons in a forest or gold in a desert.

The thing about Higham is that he's sort of a one-man Wikipedia of linear algebra. Many of the terms that he uses also have their own pages that (eventually) break the concepts down into comprehensible terms.

See https://nhigham.com/index-of-what-is-articles/ for a useful listing. Or, in an alternative form, https://github.com/higham/what-is . Notice that if you go all the way back up the rabbit hole you'll find user-friendly articles like "What is a matrix?" that clearly define the terms used farther down.

I really dig Higham's pedagogic style, in case it's not obvious.

A method which this article doesn't mention is stochastic rounding or probabilistic rounding.

Rather than striving for exact values for every computation, we make it so that the expected value is exact. For example, suppose our number system was restricted to the integers and we have incoming value 1.1, with stochastic rounding we'd round down to 1 90% of the time and 2 10% of the time giving an expected value of 1.1!

Further reading:

https://nhigham.com/2020/07/07/what-is-stochastic-rounding/