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Anything which is in any of the existing libraries. Obviously it makes
sense to prioritize and write code for the most important areas first.
- Random number generators
Includes both random number generators and routines to give various
interesting distributions.
- Statistics
- Special Functions
What I (jt) envision for this section is a collection of routines for
reliable and accurate (but not necessarily fast or efficient) estimation
of values for special functions, explicitly using Taylor series, asymptotic
expansions, continued fraction expansions, etc. As well as these routines,
fast approximations will also be provided, primarily based on Chebyschev
polynomials and ratios of polynomials. In this vision, the approximations
will be the "standard" routines for the users, and the exact (so-called)
routines will be used for verification of the approximations. It may also
be useful to provide various identity-checking routines as part of the
verification suite.
- Curve fitting
polynomial, special functions, spline
- Ordinary differential equations
- Partial differential equations
- Fourier Analysis
- Wavelets
- Matrix operations: linear equations
- Matrix operations: eigenvalues and spectral analysis
- Matrix operations: any others?
- Direct integration
- Monte carlo methods
- Simulated annealing
- Genetic algorithms
We need to think about what kinds of algorithms are basic generally
useful numerical algorithms, and which ones are special purpose
research projects. We should concentrate on supplying the former.
- Cellular automata
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