The ATLAS (Automatically Tuned Linear Algebra Software) project is an ongoing research effort focusing on applying empirical techniques in order to provide portable performance. It provides C and Fortran77 interfaces to a portably efficient BLAS implementation, as well as a few routines from LAPACK.
Frink is a calculating tool and programming language designed to help you in the real world. It tracks units of measurement throughout all calculations and ensures that answers are correct. It converts between systems of measurement, and has a huge library of physical data. It is both a simple calculator for quick calculations and a full-fledged programming language for large tasks. It draws high-quality graphics, handles conversions between time zones, currencies, and historical values of the U.S. dollar and the British pound, translates between several languages, does date/time math, and more.
MathGL is a library for making high-quality scientific graphics under Linux and Windows, fast data plotting and handling of large data arrays, working in window and console modes, and easily embedding into other programs. It has more than 40 general types of graphics for 1d, 2d, and 3d data arrays. It can export graphics to raster and vector (EPS or SVG) formats. It has an OpenGL interface and can be used from console programs. It has functions for data handling and MGL language scripting for simplification of data plotting. It has several types of transparency and smoothed lightning, vector fonts and TeX-like formula drawing, an arbitrary curvilinear coordinate system, and many other useful things.
Calc is arbitrary precision arithmetic system that uses a C-like language. It's useful as a calculator, an algorithm prototype, and as a mathematical research tool. More importantly, calc provides a machine-independent means of computation. Calc comes with a rich set of builtin mathematical and programmatic functions.
FFTW is a fast C FFT library. It includes complex, real, symmetric, multidimensional, and parallel transforms, and can handle arbitrary array sizes efficiently.It is typically faster than other freely available FFT implementations, and is even competitive with vendor-tuned libraries (benchmarks are available at the homepage). To achieve this performance, it uses novel code generation and runtime self optimization techniques (along with many other tricks).
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.
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.