Matters Computational Ideas, Algorithms, Source Code /
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...
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| Format: | Electronic eBook |
| Language: | English |
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Berlin, Heidelberg :
Springer Berlin Heidelberg,
2011.
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| Online Access: | Full Text via HEAL-Link |
Table of 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.
