LifeV is a finite element (FE) library providing implementations of state of the art mathematical and numerical methods. It serves both as a research and production library. It has already been used in medical and industrial contexts to simulate fluid structure interaction and mass transport. LifeV is the joint collaboration between four institutions: École Polytechnique Fédérale de Lausanne (CMCS) in Switzerland, Politecnico di Milano (MOX) in Italy, INRIA (REO, ESTIME) in France, and Emory University (Sc. Comp) in the U.S.A.
TooN is a very efficient numerics library for C++. The main focus of the library is efficient and safe handling of large numbers of small vector matrices and providing as much compile time checking as is possible. The library also works with large vectors and matrices and integrates easily with existing code. In addition to elementary vector and matrix operations, the library also providers linear solvers, matrix decompositions, optimization, and wrappers around LAPACK.
FLENS is short for Flexible Library for Efficient Numerical Solutions. This C++ can be used as a builing block for the implementation of other (higher-level) numerical libraries or numerical applications. It is a C++ library (requires a C++11 conform compiler). Easy install, as FLENS is headers only. It gives you Matrix/vector types for dense linear algebra; a generic (i.e. templated) implementation of BLAS; and a generic reimplementation of LAPACK. If high performance BLAS libraries like ATLAS, GotoBLAS, etc. are available, you simply can link against them and boost performance.
The Graphical Models Toolkit (GMTK) is a toolkit for rapidly prototyping statistical models using dynamic graphical models (DGMs) and dynamic Bayesian networks (DBNs). It can be used for speech and language processing, bioinformatics, activity recognition, and any time series application. It features exact and approximate inference, many built-in factors including dense, sparse, and deterministic conditional probability tables, native support for ARPA backoff-based factors and factored language models, parameter sharing, gamma and beta distributions, dense and sparse Gaussian factors, heterogeneous mixtures, deep neural network factors, and time-inhomogeneous trellis factors, arbitrary order embedded Markov chains, a GUI graph viewer, and much more.
Meta.Numerics is a Mono-compatible .NET library for scientific and numerical programming. It includes functionality for matrix algebra (including SVD, non-symmetric eigensystems, and sparse matrices), special functions of real and complex numbers (including Bessel functions and the complex error function), statistics and data analysis (including PCA, logistic and nonlinear regression, statistical tests, and nonuniform random deviates), and signal processing (including arbitrary-length FFTs).
The Shared Scientific Toolbox is a library that facilitates development of efficient, modular, and robust scientific/distributed computing applications in Java. It features multidimensional arrays with extensive linear algebra and FFT support, an asynchronous, scalable networking layer, and advanced class loading, message passing, and statistics packages.