The library covers a wide range of topics in numerical computing. Routines are available for the following areas,
| Complex Numbers | Roots of Polynomials
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| Special Functions | Vectors and Matrices
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| Permutations | Combinations
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| Sorting | BLAS Support
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| Linear Algebra | CBLAS Library
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| Fast Fourier Transforms | Eigensystems
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| Random Numbers | Quadrature
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| Random Distributions | Quasi-Random Sequences
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| Histograms | Statistics
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| Monte Carlo Integration | N-Tuples
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| Differential Equations | Simulated Annealing
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| Numerical Differentiation | Interpolation
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| Series Acceleration | Chebyshev Approximations
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| Root-Finding | Discrete Hankel Transforms
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| Least-Squares Fitting | Minimization
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| IEEE Floating-Point | Physical Constants
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| Basis Splines | Wavelets
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The use of these routines is described in this manual. Each chapter provides detailed definitions of the functions, followed by example programs and references to the articles on which the algorithms are based.
Where possible the routines have been based on reliable public-domain packages such as FFTPACK and QUADPACK, which the developers of GSL have reimplemented in C with modern coding conventions.