The Top Ten Algorithms of the Century
Dongarra and Sullivan

Jack Dongarra and Francis Sullivan published a list of "The Top Ten Algorithms of the Century." Their list included:

1. the Monte Carlo method or Metropolis algorithm, devised by John von Neumann, Stanislaw Ulam, and Nicholas Metropolis, 1946;
2. the simplex method of linear programming, developed by George Dantzig, 1947;
3. the Krylov Subspace Iteration method, developed by Magnus Hestenes, Eduard Stiefel, and Cornelius Lanczos, 1950;
4. the Householder matrix decomposition, developed by Alston Householder, 1951;
5. the Fortran compiler, developed by a team lead by John Backus, 1957;
6. the QR algorithm for eigenvalue calculation, developed by J Francis, 1959;
7. the Quicksort algorithm, developed by Anthony Hoare, 1962;
8. the Fast Fourier Transform, developed by James Cooley and John Tukey, 1965;
9. the Integer Relation Detection Algorithm, developed by Helaman Ferguson and Rodney Forcade, 1977; (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, 1987; (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. Jack Dongarra, Francis Sullivan,
   Top Ten Algorithms of the Century,
   Computing in Science and Engineering,
   Volume 2, Number 1, January/February 2000, pages 22-23.
2. Barry Cipra,
   The Best of the 20th Century: Editors Name Top 10 Algorithms
   SIAM News,
   Volume 33, Number 4, May 2000, page 1.
3. Dan Givoli,
   The Top 10 Computational Methods of the 20th Century,
   IACM Expressions,
   Number 11, September 2001, pages 5-9.