The Top Ten Algorithms of the Century

1. the Monte Carlo method or Metropolis algorithm, devised by John von Neumann,
   Stanislaw Ulam, and Nicholas Metropolis;
2. the simplex method of linear programming, developed by George Dantzig;
3. the Krylov Subspace Iteration method, developed by Magnus Hestenes, Eduard
   Stiefel, and Cornelius Lanczos;
4. the Householder matrix decomposition, developed by Alston Householder;
5. the Fortran compiler, developed by a team lead by John Backus;
6. the QR algorithm for eigenvalue calculation, developed by J Francis;
7. the Quicksort algorithm, developed by Anthony Hoare;
8. the Fast Fourier Transform, developed by James Cooley and John Tukey;
9. the Integer Relation Detection Algorithm, developed by Helaman Ferguson and
   Rodney Forcade; (given N real values X_I, is there a nontrivial set of
   integer coefficients A_I so that sum ( 1 <= I <= N )
   A_I * X_I = 0?
10. the fast Multipole algorithm, developed by Leslie Greengard and Vladimir
    Rokhlin; (to calculate gravitational forces in an N-body problem normally
    requires N^2 calculations. The fast multipole method uses order N calculations,
    by approximating the effects of groups of distant particles using multipole
    expansions)

Reference 1:

Dongarra and Sullivan, Top Ten Algorithms of the Century, Computing in Science and Engineering, January/February 2000.

 

Reference 2:

Barry Cipra, The Best of the 20th Century: Editors Name Top 10 Algorithms SIAM News, Volume 33, Number 4, May 2000, page 1.