LINPACK_S, a FORTRAN77 library which can solve systems of linear equations for a variety of matrix types and storage modes, by Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart.
LINPACK has officially been superseded by the LAPACK library. The LAPACK library uses more modern algorithms and code structure. However, the LAPACK library can be extraordinarily complex; what is done in a single LINPACK routine may correspond to 10 or 20 utility routines in LAPACK. This is fine if you treat LAPACK as a black box. But if you wish to learn how the algorithm works, or to adapt it, or to convert the code to another language, this is a real drawback. This is one reason I still keep a copy of LINPACK around.
Versions of LINPACK in various arithmetic precisions are available through the NETLIB web site.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
LINPACK_S is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.
BLAS1_S, a FORTRAN77 library which contains basic linear algebra routines for vector-vector operations, using single precision real arithmetic.
LAPACK_EXAMPLES, a FORTRAN77 program which demonstrates the use of the LAPACK linear algebra library.
LINPACK_BENCH, a FORTRAN90 program which measures the time taken by LINPACK to solve a particular linear system.
LINPACK_C, a FORTRAN90 library which is a version of LINPACK for single precision complex arithmetic.
LINPACK_D, a FORTRAN90 library which is a version of LINPACK for double precision real arithmetic.
LINPACK_Z, a FORTRAN90 library which is a version of LINPACK for double precision complex arithmetic.
LINPLUS, a FORTRAN977 library which carries out some linear algebra operations on matrices in a variety of formats.
NMS, a FORTRAN90 library which includes LINPACK.
SLATEC, a FORTRAN90 library which includes LINPACK.
TEST_MAT, a FORTRAN90 library which defines test matrices, some of which have known determinants, eigenvalues and eigenvectors, inverses and so on.
Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart.