GNU Multi-Precision Library is a library for doing arbitrary-precision arithmetic.

GNU Scientific Library, a popular, free numerical analysis library implemented in C.

FFTW (Fastest Fourier Transform in the West) is a software library for computing Fourier and related transforms.

BLOPEX (Block Locally Optimal Preconditioned Eigenvalue Xolvers) is an open-sourcelibrary for the scalable (parallel) solution of eigenvalue problems.

It can be used from C, C++, Fortran, and a dedicated GNU Octave package.

librsb is an open source library for high performance sparse matrix computations providing multi-threaded primitives to build iterative solvers (implements also the Sparse BLAS standard).

It also can be used with batch orientation.

APIs, functions and libraries can be called from many platforms, including high level engineering programs, where functions are, in many cases, seamlessly interpreted and integrated in similar fashion to MATLAB. GNU Octave is an open source high level programming language and library, including a command line interface and GUI, analogous to commercial alternatives such as Maple, MATLAB, Mathematica, etc.The NAG Library is a collection of mathematical and statistical routines for multiple programming languages (C, C++, Fortran, Visual Basic, Java, Python and C#) and packages (MATLAB, Excel, R, LabVIEW).IMSL Numerical Libraries are libraries of numerical analysis functionality implemented in standard programming languages like C, Java, C#.ArrayFire is a high performance open source software library for parallel computing with an easy-to-use API.ALGLIB is an open source numerical analysis library which may be used from C++, C#, FreePascal, Delphi, VBA.As we find comprehensive surveys rarely available, there is almost always (at least initially) a difficult choice among a number of possible libraries.Often it tends to be at the discretion of the user based on his own taste and comforts, only due to the lack of proper information.

Fitpack fortran library