The ATLAS (Automatically Tuned Linear Algebra Software) project is an ongoing research effort focusing on applying empirical techniques in order to provide portable performance. At present, it provides C and Fortran77 interfaces to a portably efficient BLAS implementation, as well as a few routines from LAPACK.
FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data (as well as of even/odd data, i.e. the discrete cosine/sine transforms or DCT/DST). We believe that FFTW, which is free software, should become the FFT library of choice for most applications.
This library package provides several forward error correction (FEC) decoders and accelerated primitives useful in digital signal processing (DSP). Except for the Reed-Solomon codecs, these functions take full advantage of the MMX, SSE and SSE2 SIMD instruction sets on Intel/AMD IA-32 processors and the Altivec/VMX/Velocity Engine SIMD instruction set on the G4 and G5 PowerPC.
GNU Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command line interface for solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with Matlab. It may also be used as a batch-oriented language.