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The Art of Computer Programming, Volume 2

Seminumerical Algorithms , third Edition

Gebonden Engels 1997 9780201896848
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The second volume offers a complete introduction to the field of seminumerical algorithms, with separate chapters on random numbers and arithmetic. The book summarizes the major paradigms and basic theory of such algorithms, thereby providing a comprehensive interface between computer programming and numerical analysis. Particularly noteworthy in this third edition is Knuth's new treatment of random number generators, and his discussion of calculations with formal power series.


Aantal pagina's:704
Hoofdrubriek:IT-management / ICT


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Over Donald Knuth

Donald E. Knuth was born on January 10, 1938 in Milwaukee, Wisconsin. He studied mathematics as an undergraduate at Case Institute of Technology, where he also wrote software at the Computing Center. The Case faculty took the unprecedented step of awarding him a Master's degree together with the B.S. he received in 1960. After graduate studies at California Institute of Technology, he received a Ph.D. in Mathematics in 1963 and then remained on the mathematics faculty. Throughout this period he continued to be involved with software development, serving as consultant to Burroughs Corporation from 1960-1968 and as editor of Programming Languages for ACM publications from 1964-1967. He joined Stanford University as Professor of Computer Science in 1968, and was appointed to Stanford's first endowed chair in computer science nine years later. As a university professor he introduced a variety of new courses into the curriculum, notably Data Structures and Concrete Mathematics. In 1993 he became Professor Emeritus of The Art of Computer Programming. He has supervised the dissertations of 28 students. Knuth began in 1962 to prepare textbooks about programming techniques, and this work evolved into a projected seven-volume series entitled The Art of Computer Programming. Volumes 1-3 first appeared in 1968, 1969, and 1973. Having revised these three in 1997, he is now working full time on the remaining volumes. Approximately one million copies have already been printed, including translations into six languages.

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Generating Uniform Random Numbers.

The Linear Congruential Method.
Other Methods.

Statistical Tests.

General Test Procedures for Studying Random Data.
Empirical Tests.
Theoretical Tests.
The Spectral Test.

Other Types of Random Quantities.

Numerical Distributions.
Random Sampling and Shuffling.

What Is a Random Sequence?

4. Arithmetic.
Positional Number Systems.
Floating Point Arithmetic.

Single-Precision Calculations.
Accuracy of Floating Point Arithmetic.
Double-Precision Calculations.
Distribution of Floating Point Numbers.

Multiple Precision Arithmetic.

The Classical Algorithms.
Modular Arithmetic.
How Fast Can We Multiply?.

Radix Conversion.
Rational Arithmetic.

The Greatest Common Divisor.
Analysis of Euclid's Algorithm.
Factoring into Primes.

Polynomial Arithmetic.

Division of Polynomials.
Factorization of Polynomials.
Evaluation of Powers.
Evaluation of Polynomials.

Manipulation of Power Series.
Answers to Exercises.

Appendix A: Tables of Numerical Quantities.
Fundamental Constants (decimal).
Fundamental Constants (octal).
Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers.

Appendix B: Index to Notations.
Index and Glossary.

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