from SIAM News, Volume 33, Number 4
The Best of the 20th Century: Editors Name Top 10 Algorithms
By Barry A. Cipra
Algos is the Greek word for pain. Algor is Latin, to be cold. Neither is the root for algorithm, which stems instead from alKhwarizmi, the n
Math. Ann. 261, 515-534 (1982)
Imam
9 Springer-Verlag 1982
Factoring Polynomials with Rational Coefficients
A. K. Lenstra 1, H. W. Lenstra, Jr. 2, and L. Lovfi~z3
I
1 Mathematisch Centrum, Kruislaan 413, NL-1098 SJ Amsterdam, The Netherlands
2 Mathematisc
THE
QRALGORITHM
After a brief sketch of the early days of eigenvalue hunting, the author describes the QR
Algorithm and its major virtues. The symmetric case brings with it guaranteed convergence
and an elegant implementation. An account of the impressive
THE AN ALGORITHM
FFT:
THE WHOLE
FAMILY USE
CAN
The fast Fourier transform is one of the fundamental algorithm families in digital
information processing. The author discusses its past, present, and future, along with its
important role in our current digi
KRYLOV
SUBSPACE
ITERATION
This survey article reviews the history and current importance of Krylov subspace iteration
algorithms.
S
ince the early 18OOs, researchers have
considered iteration methods an attractive means for approximating the solntions of
THE
DECOMPOSITIONAL
APPROACH
TO MKTRIX
COMPUTATION
The introduction of matrix decomposition into numerical linear algebra revolutionized
matrix computations. This article outlines the decompositional approach, comments on its
history, and surveys the six
JOURNAL O F THE A M E R I C A N
STATISTICAL ASSOCIATION
Number 167
S E P T E M B E R 1949
Volume 44
T H E MONTE CARL0 METHOD
NICHOLAS
METROPOLIS S. ULAM
AND
Los Alamos Laboratory
We shall present here the motivation and a general description of a method d
Programming
Techniques
S. L. Graham, R. L. Rivest
Editors
Implementing
Quicksort Programs
Robert Sedgewick
Brown University
This paper is a practical study of how to implement
the Quicksort sorting algorithm and its best variants on
real computers, includ
THE
(DANTZIG)
SIMFLEXMETHOD
FOR LINEAR
PROGRAMMING
George Dantzig created a simplex algorithm to solve linear programs for planning and
decision-making in large-scale enterprises. The algorithms success led to a vast array of
specializations and generaliz
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INTEGER
&LATION DETECTION
Practical algorithms for integer relation detection have become a staple in the emerging
discipline of experimental mathematics-using modern computer technology to explore
mathematical questions. After briefly discussing the prob
THE
METROPOLIS
ALGORITHM
The Metropolis Algorithm has been the most successful and influential of all the members of
the computational species that used to be called the Monte Carlo Method. Today, topics
related to this algorithm constitute an entire fiel
Space/Time Trade-offs in
Hash Coding with
Allowable Errors
BURTON H. BLOOM
Computer Usage Company, Newton Upper Falls, Mass.
In this paper trade-offs among certain computational factors
in hash coding are analyzed. The paradigm problem considered is that
THE M ~ T I P O L E
FAST
ALGORITHM
Accurate computation of the mutual interactions of N particles through electrostatic or
gravitational forces has impeded progress in many areas of simulation science. The fast
multipole algorithm provides an efficient sc
GUEST EDITORS
INTRODUCTION
the Top
I
n putting together this issue of Computing in
Science & Engineering, we knew three things:
it would be difcult to list just 10 algorithms;
it would be fun to assemble the authors and
read their papers; and, whatever we
An Algorithm for the Machine Calculation of
Complex Fourier Series
By James W. Cooley and John W. Tukey
An eﬂicient method for the calculation of the interactions of a 2'" factorial ex-
periment was introduced by Yates and is widely known by his name. The
A PERSPECTIVE QUICKSORT
ON
This article introduces the basic Quicksort algorithm and gives a flavor of the richness of its
complexity analysis. The author also provides a glimpse of some of its generalizations to
parallel algorithms and computational geom
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