Top 10: Los mejores algoritmos del Siglo XX

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1. Top 10: Los mejores algoritmos del siglo XX Elizabeth Ramirez @eramirem
2. Ingeniera Electrónica Applied Mathematician Applied Scientist
3. Algoritmo: Viene de Muhammad ibn Musa al-Khwarizmi El mismo del libro “Al-jabr wa'l muqabalah” también conocido como Álgebra.
4. January/February 2000 issue of Computing in Science & Engineering. https://ieeexplore.ieee.org/xpl/tocr esult.jsp?isnumber=17639 •
5. • Metropolis Algorithm • Simplex for Linear Programming • Krylov Subspaces Algorithm • Matrix Decomposition Algorithm • The Fortran Optimizing Compiler • QR Algorithm • Quicksort Algorithm • Fast Fourier Transform Algorithm • Integer Relation Detection • Fast Multipole Method (Los tachados se los quedo debiendo)
6. 1946: Metropolis Algorithm A.K.A Monte Carlo. John von Neumann, Stan Ulam, and Nick Metropolis at Los Alamos National Lab. By the Strong Law of Large Numbers: In general:
7. 1946: Metropolis Algorithm A.K.A Monte Carlo. For multidimensional definite integrals. Given a set of N uniform random variables
8. 1946: Metropolis Algorithm A.K.A Monte Carlo. Probability Distributions. E.g. Queue Theory, single server recursion: S: Service time T: Interarrival time expected delay of the 5th customer.
9. 1946: Metropolis Algorithm A.K.A Monte Carlo.
10. 1950: Krylov Subspaces Magnus Hestenes, Eduard Stiefel, and Cornelius Lanczos, from the Institute for Numerical Analysis at the National Bureau of Standards. Solve , A.K.A. most ubiquitous problem in Scientific Computing. Problem: when A is huge. E.g. Gaussian Elimination: Solution: iterative methods! Krylov subspace of dimension k, with
11. 1950: Krylov Subspaces Method searches a good approximation to the solution in the subspace, such that
12. 1951: Matrix Decomposition Alston Householder of Oak Ridge National Laboratory One of the most important ideas in Linear Algebra. Fundamental Decompositions: Cholesky, pivoted LU, QR, spectral, Schur, and SVD.
13. 1951: Matrix Decomposition Pivoted LU.
14. 1959–61: QR Algorithm J.G.F. Francis of Ferranti Ltd., London. Guess which problem we’re solving again? Yes, Construct a set of orthonormal vectors that span each of the subspaces
15. 1959–61: QR Algorithm
16. 1959–61: QR Algorithm
17. 1959–61: Fast Fourier Transform James Cooley of the IBM T.J. Watson Research Center and John Tukey of Princeton University and AT&T Bell Labs. Described by this guy (G. Strang) as “the most important numerical algorithm of our lifetime”. Takes discrete FT from to Given, the DFT is defined as: G
18. 1959–61: Fast Fourier Transform
19. Gracias!