Nick Higham
nhigham.com · Personal blog · on HN since 2020
Nick Higham, a numerical analysis professor, writes a 'What Is?' series explaining matrix and numerical computing concepts.
What HN saysCommenters cite it for numerical topics such as half-precision formats and the nearest positive semidefinite matrix, and list it among good math blogs.
32HN people shared it
15linked it in comments
45stories submitted
1.5Kstory points
2 years agolast shared
2020people per year2026
Most-shared posts
- 1What Is the Complex Step Approximation? (2020)4 people · 14 points · first shared 2021 · 2 comments on HN
- 2Nick Higham: 'What Is?' Series3 people · 2 points · first shared 2022 · discussion on HN
- 3The Power of Bidiagonal Matrices2 people · 3 points · first shared 2023 · discussion on HN
- 4What Is Gershgorin’s Theorem?2 people · 3 points · first shared 2022 · discussion on HN
- 5What Is a Cholesky Factorization?2 people · 3 points · first shared 2020 · discussion on HN
- 6What Is Numerical Stability?2 people · 3 points · first shared 2020 · discussion on HN
- 7What Is a Hessenberg Matrix?2 people · 2 points · first shared 2023 · discussion on HN
- 8What Is Stochastic Rounding?2 people · 1 points · first shared 2020 · discussion on HN
- 9Homepage2 people · first shared 2021
- 10Seven sins of numerical linear algebra1 people · 333 points · first shared 2022 · 72 comments on HN
- 11The big six matrix factorizations1 people · 268 points · first shared 2022 · 78 comments on HN
- 12What is an eigenvalue?1 people · 262 points · first shared 2022 · 154 comments on HN
- 13The Princeton Companion to Applied Mathematics1 people · 215 points · first shared 2024 · 34 comments on HN
- 14Org Mode Syntax Cheat Sheet (2017)1 people · 132 points · first shared 2024 · 69 comments on HN
- 15Can We Solve Linear Algebra Problems at Extreme Scale and Low Precisions?1 people · 95 points · first shared 2021 · 25 comments on HN
What HN people wrote when they linked it
toomuchtodo · 2024-01-24
https://nhigham.com/
https://en.wikipedia.org/wiki/Nicholas_Higham
octocop · 2023-11-03
Inspired by a great blog post by Nick Higham https://nhigham.com/2018/12/03/half-precision-arithmetic-fp16-versus-b…
jjgreen · 2021-11-30
Terrence Tao https://terrytao.wordpress.com/
Nick Higham https://nhigham.com/
Infinity315 · 2024-05-25
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/
pvitz · 2024-04-28
In my case, I am applying this in the calibration of instantaneous correlation matrices. His relevant papers can be found at [0]. It was really helpful that he also published MATLAB code of most of his algorithms.
[0] https://nhigham.com/correlation-matrices/
abhgh · 2024-04-28
Thanks for mentioning that. It's a problem I occasionally need to solve and based on your comment, I found this helpful write up by Nick Higham [1].
[1] https://nhigham.com/2021/01/26/what-is-the-nearest-positive-semidefini…
krosaen · 2024-03-04
Wow, apparently published his last post, "What Is the Spectral Radius of a Matrix?" just 8 days before his passing. Legend.
https://nhigham.com/2024/01/
Bostonian · 2024-01-22
Higham, who contributed code to the NAG library and Matlab, had a good blog on applied mathematics, numerical linear algebra, and software at https://nhigham.com/blog/.
shusaku · 2023-11-23
This might help: https://nhigham.com/2020/06/09/what-is-a-matrix-function/
soegaard · 2023-01-08
FWIW there is an ISO Standard:
> ISO 80000-2:2009
> Quantities and units — Part 2: Mathematical signs and symbols to be used in the natural sciences and technology
https://nhigham.com/2016/01/28/typesetting-mathematics-according-to-th…
CamperBob2 · 2022-11-08
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.
lr1970 · 2022-10-12
Also, please check other posts in Professor Nick Higham's blog. Especially his wonderful and accessible "What is ..." series of articles [0]
[0] https://nhigham.com/index-of-what-is-articles/
defrost · 2022-10-12
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-mathem…
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.
heinrichhartman · 2022-05-18
As it turns out, the author does cover the rank-decomposition (under the name "Rank-Revealing Factorization") in his blog as well:
https://nhigham.com/2021/05/19/what-is-a-rank-revealing-factorization/