Octave is a public domain clone of matlab. It is about 95% compatible with Matlab.
OpenBLAS is an optimized BLAS library based on GotoBLAS2 1.13 BSD version.
PETSc, pronounced PET-see (the S is silent), is a suite of data structures and routines for the scalable (parallel) solution of scientific applications modeled by partial differential equations.
R is a free software environment for statistical computing and graphics.
ROOT is a data analysis framework.
SCOTCH is a software package and libraries for sequential and parallel graph partitioning, static mapping, and sparse matrix block ordering, and sequential mesh and hypergraph partitioning.
SPECFUN is a FORTRAN90 library which evaluates certain special functions, by William Cody and Laura Stoltz.
SuiteSparse is a suite of sparse matrix algorithms.