Some of these implementations are the result of courses on Scientific Computing (``Wissenschaftliches Rechnen'') and are mostly intended to demonstrate how to implement certain algorithms in R/S. Others are implementations of algorithms found in textbooks.

- Root finding and minimization of univariate functions, e.g. Newton-Raphson, Brent-Dekker, Fibonacci or `golden ratio' search.
- Handling polynomials, including roots and polynomial fitting, e.g. Laguerre's and Muller's methods.
- Interpolation and function approximation, barycentric Lagrange interpolation, Pade and rational interpolation, Chebyshev or trigonometric approximation.
- Some special functions, e.g. Fresnel integrals, Riemann's Zeta or the complex Gamma function, and Lambert's W computed iteratively through Newton's method.
- Special matrices, e.g. Hankel, Rosser, Wilkinson
- Numerical differentiation and integration, Richardson approach and ``complex step'' derivatives, adaptive Simpson and Lobatto integration and adaptive Gauss-Kronrod quadrature.
- Solvers for ordinary differential equations and systems, Euler-Heun, classical Runge-Kutta, ode23, or predictor-corrector method such as the Adams-Bashford-Moulton.
- Some functions from number theory, such as primes and prime factorization, extended Euclidean algorithm.
- Sorting routines, e.g. recursive quickstep.
- Several functions for string manipulation and regular search, all wrapped and named similar to their Matlab analogues.

It serves two main goals:

- Collecting R scripts that can be demonstrated in courses on `Numerical Analysis' or `Scientific Computing' using R/S as the chosen programming language.
- Wrapping functions with appropriate Matlab names to simplify porting programs from Matlab or Octave to R.
- Providing an environment in which R can be used as a full-blown numerical computing system.

Besides that, many of these functions could be called in R applications as they do not have comparable counterparts in other R packages (at least at this moment, as far as I know).

All referenced books have been utilized in one way or another. Web links have been provided where reasonable.

Arndt, J. (2010). Matters Computational: Ideas, Algorithms, Source Code. Springer-Verlag, Berlin Heidelberg Dordrecht. FXT: a library of algorithms: http://www.jjj.de/fxt/.

Cormen, Th. H., Ch. E. Leiserson, and R. L. Rivest (2009). Introduction to Algorithms. Third Edition, The MIT Press, Cambridge, MA.

Encyclopedia of Mathematics (2012). Editor-in-Chief: Ulf Rehmann. http://www.encyclopediaofmath.org/.

Gautschi, W. (1997). Numerical Analysis: An Introduction. Birkhaeuser, Boston.

Gentle, J. E. (2009). Computational Statistics. Springer Science+Business Media LCC, New York.

Hazewinkel, M., Editor (2002). Encyclopaedia of Mathematics. Springer-Verlag, Berlin Heidelberg New York. http://eom.springer.de/.

MathWorld.com (2011). Matlab Central: http://www.mathworks.com/matlabcentral/. Mathtools.net: http://www.mathtools.net/.

NIST: National Institute of Standards and Technology. Olver, F. W. J., et al. (2010). NIST Handbook of Mathematical Functions. Cambridge University Press. Internet: NIST Digital Library of Mathematical Functions, http://dlmf.nist.gov/; Dictionary of Algorithms and Data Structures, http://www.nist.gov/; Guide to Available Mathematical Software, http://gams.nist.gov/

Press, W. H., S. A. Teukolsky, W. T Vetterling, and B. P. Flannery (2007). Numerical Recipes: The Art of Numerical Computing. Third Edition, incl. Numerical Recipes Software, Cambridge University Press, New York. http://www.nrbook.com/a/bookcpdf.php [chapters], or http://apps.nrbook.com/c/index.html [pages].

Quarteroni, A., R. Sacco, and F. Saleri (2007). Numerical Mathematics. Second Edition, Springer-Verlag, Berlin Heidelberg.

Skiena, St. S. (2008). The Algorithm Design Manual. Second Edition, Springer-Verlag, London. The Stony Brook Algorithm Repository: http://www.cs.sunysb.edu/~algorith/.

Stoer, J., and R. Bulirsch (2002). Introduction to Numerical Analysis. Third Edition, Springer-Verlag, New York.

Strang, G. (2007). Computational Science and Engineering. Wellesley-Cambridge Press. Matlab Codes: http://www-math.mit.edu/cse/

Weisstein, E. W. (2003). CRC Concise Encyclopedia of Mathematics. Second Edition, Chapman & Hall/CRC Press. Wolfram MathWorld: http://mathworld.wolfram.com/.

Zhang, S., and J. Jin (1996). Computation of Special Functions. John Wiley & Sons.

```
## Not run:
# ## See examples in the help files for all functions.
# ## End(Not run)
```

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