Re: [Rd] Task View on Numerical Analysis and Differential Equations

From: Ravi Varadhan <rvaradhan_at_jhmi.edu>
Date: Thu, 08 Mar 2012 15:40:38 +0000

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?

ink2">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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