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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).
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