MATH 6140 - The Top Ten Algorithms from the 20th Century

Alex Townsend, spring 2017.

In the January/February 2000 issue of Computing in Science and Engineering, Jack Dongarra and Francis Sullivan selected 10 algorithms with the greatest influence on science, numerical analysis, and engineering in the 20th century. In March 2016, Nick Higham (SIAM president, 2017-2018) presented a slightly revised list. In no particular order, the list is:

1. Newton and quasi-Newton methods,
2. Matrix factorizations (LU, Cholesky, QR)
3. Singular value decomposition, QR and QZ algorithms,
4. Monte-Carlo methods,
5. Fast Fourier transform,
6. Krylov subspace methods,
7. JPEG,
8. PageRank,
9. Simplex method, and
10. Kalman filter.

We will cover the motivations, ideas, history, and future impact of these ten algorithms. Honorable mentions are the fast multipole method, quicksort, and bootstrapping that may be covered if time permits.