几乎包含了所有的数值分析函数

The package encompasses functions from all areas of numerical analysis, for example:

• 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 trigonomet-ric 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 integra-tion 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.

Besides that, many of these functions could be called in R applications as they do not have compa-rable counterparts in R packages (at least at this moment).