[Rd] Task View on Numerical Analysis and Differential Equations

[Ravi Varadhan]

Dear Hans Werner,

I like the idea overall.  Nothing prevents you from doing this, but you should be committed to getting it up and running and then keeping it updated.

In addition to concurring with Berend's comments, I also would like to mention that numerical analysis (NA) is an extremely broad category.  I am not sure how to restrict that in order to make the taskview manageable.  How about including (i) convergence acceleration of sequences, (ii) fourier transforms/wavelets, (iii) function approximation and special functions of mathematical physics?

Best regards,
Ravi

P.S. I have a package called "eiginv" for solving certain types of inverse eigenvalue problems (e.g., generating a matrix of a specific structure with a given set of eigenvalues)


-----Original Message-----
From: r-devel-bounces at r-project.org [mailto:r-devel-bounces at r-project.org] On Behalf Of Berend Hasselman
Sent: Thursday, March 08, 2012 9:59 AM
To: Hans W Borchers
Cc: r-devel at r-project.org
Subject: Re: [Rd] Task View on Numerical Analysis and Differential Equations


On 08-03-2012, at 12:16, Hans W Borchers wrote:

> I am wondering if it would be time to have a new Task View, this time 
> for the subject of "Numerical Analysis and Differential Equations".
> The list of packages possibly appearing in such a task view is already 
> quite long and could, for example, include:
> 
> Numerical Analysis and Linear Algebra
> 
> Bessel        Bessel Functions Computations and Approximations
> cubature      Adaptive multivariate integration over hypercubes
> elliptic      Elliptic and related functions
> expm          Matrix exponential, logarithm, etc.
> fdim	      Functions for calculating fractal dimension
> gaussquad     Collection of functions for Gaussian quadrature
> gmp           Multiple precision arithmetic
> gsl           Wrapper for the Gnu Scientific Library
> hypergeo      The hypergeometric function
> irlba         Fast partial SVD by Lanczos bidiagonalization
> matlab        MATLAB emulation package
> multipol      Multivariate polynomials
> numDeriv      Accurate numerical derivatives
> onion         Octonions and quaternions
> orthogonalsplinebasis  Orthogonal Bspline basis functions orthopolynom  
> Functions for orthogonal and orthonormal polynomials
> polspline     Polynomial spline routines
> polynom       Implement a class for univariate polynomial manipulations
> PolynomF      Polynomials in R
> pracma        Practical numerical math functions
> pspline       Penalized smoothing splines
> quaternions   Arithmetics and linear algebra with quaternions
> R2Cuba        Multidimensional numerical integration
> RcppArmadillo Rcpp integration for Armadillo templated linear algebra library
> RcppEigen	  Rcpp integration for the Eigen templated linear algebra library
> RcppOctave    Rcpp integration of Octave
> R.matlab	  Read and write of MAT files and R-to-Matlab connectivity
> Rmpfr	      Multiple precision floating-point reliable
> sparseGrid    Sparse grid integration in R
> spuRs         Functions and datasets scientific programming and simulation
> sspline       Smoothing splines on the sphere
> stinepack     Stineman: consistently well behaved method of interpolation
> svd           Interfaces to various state-of-art SVD and eigensolvers
> voronoi       Methods and applications related to Voronoi tessellations
> wavelets...
> 
> Simulation and Differential Equations
> 
> bvpSolve	  Solvers for boundary value problems of ODEs
> ddesolve      Solver for Delay Differential Equations
> deSolve       General solvers for initial value problems of ordinary
>              differential equations (ODE), partial differential equations
>              (PDE), differential algebraic equations (DAE), and delay
>              differential equations (DDE)
> deTestSet	  Testset for differential equations
> odesolve	  Solvers for Ordinary Differential Equations
> PBSddesolve	  Solver for Delay Differential Equations
> rootSolve     Root finding, equilibrium and steady-state analysis of ODEs
> sde           Simulation and Inference for Stochastic Differential Equations
> Sim.DiffProc  Simulation of diffusion processes
> simecol       Simulation of ecological and other dynamic systems
> 
> and probably many more in the end. I left out the optimization 
> packages deliberately, but of course there would be a strong hint to 
> that task view.


If you put pracma in "Numerical Analysis and Linear Algebra", then I feel you should also include  BB and nleqslv under that heading. Both of these do things that can be classified as Numerical Analysis. And both can of course also be used for simulation.


BB  solve  (sparse) systems of non linear equations using spectral gradient methods nleqslv solve systems of nonlinear equations combining global strategies with a Broyden or Newron method.

Berend

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