(Note: If you find any other quality software packages for numerical computing, please let me know and I will link to them on this page.)
· Matrix derivatives from John Dattoro.
· The GNU Scientific Library (GSL) is an excellent library for numerical and scientific computing.
· The GNU Linear Programming Kit (GLPK) is an excellent library for linear programming and mixed integer programming. It can be run from the command line as well as in library form through a C API.
· GNU MathProg is a language for specifying optimization programs that can be read through GLPK and other solvers.
· libLBFGS is a package for large scale unconstrained optimization using a low-memory BFGS quasi-Newton method.*
· KrisLibrary is an internal library developed in my lab that contains a variety of linear algebra, optimization, root-finding routines, and interfaces to GLPK and GSL in a consistent object oriented interface.
· MOSEK: a commercial-grade solver for LPs, QPs, SOCPs with a free academic license.
· GAMS: a modeling system for LPs, QPs, and NLPs with a free demo mode that works on problems of limited size.
· WEKA: a data mining/machine learning toolbox for Java.
· OpenBUGS: A language for defining Bayesian networks and performing inference using Gibbs sampling.
* I have not tested this software so I can’t attest to its quality.