Matters Computational : Ideas, Algorithms, Source Code / by Jörg Arndt.

Format:

Book

Author/Creator:

Arndt, Jörg, 1964- author.

Contributor:

SpringerLink (Online service)

Series:

Computer Science (Springer-11645)

Language:

English

Subjects (All):

Algorithms.

Algorithm Analysis and Problem Complexity.

Local Subjects:

Algorithm Analysis and Problem Complexity.

Physical Description:

1 online resource (XIV, 978 pages) : 475 illustrations

Edition:

First edition 2011.

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2011.

System Details:

text file PDF

Summary:

This book provides algorithms and ideas for computationalists. Subjects treated include low-level algorithms, bit wizardry, combinatorial generation, fast transforms like the Fourier transform, and fast arithmetic for both real numbers and finite fields. Various optimization techniques are described and the actual performance of many given implementations is examined. The focus is on material that does not usually appear in textbooks on algorithms. The implementations are done in C++ and the GP language, written for POSIX-compliant platforms such as the Linux and BSD operating systems.

Contents:

Low level algorithms

Bit wizardry

Permutations and their operations

Sorting and searching

Data structures

Combinatorial generation

Conventions and considerations

Combinations

Compositions

Subsets

Mixed radix numbers

Permutations

Multisets

Gray codes for string with restrictions

Parenthesis strings

Integer partitions

Set partitions

Necklaces and Lyndon words

Hadamard and conference matrices

Searching paths in directed graphs

Fast transforms

The Fourier transform

Convolution, correlation, and more FFT algorithms

The Walsh transform and its relatives

The Haar transform

The Hartley transform

Number theoretic transforms (NTTs)

Fast wavelet transforms

Fast arithmetic

Fast multiplication and exponentiation

Root extraction

Iterations for the inversion of a function

The AGM, elliptic integrals, and algorithms for computing

Logarithm and exponential function

Computing the elementary functions with limited resources

Numerical evaluation of power series

Cyclotomic polynomials, product forms, and continued fractions

Synthetic Iterations.-. Algorithms for finite fields

Modular arithmetic and some number theory

Binary polynomials

Shift registers

Binary finite fields

The electronic version of the book

Machine used for benchmarking

The GP language

Bibliography

Index.

Other Format:

Printed edition:

ISBN:

978-3-642-14764-7

9783642147647

Access Restriction:

Restricted for use by site license.