LINPACK

LINPACK is a software library written in Fortran intended for performing numerical linear algebra on digital computers. It was a collaborative project led by J. J. Dongarra, C. B. Moler, J. R. Bunch, and G. W. Stewart, and released in 1979. The library focuses on providing routines for solving linear systems of equations and linear least squares problems.

LINPACK is structured around the BLAS (Basic Linear Algebra Subprograms) routines, which provide optimized kernels for common vector and matrix operations. By building on BLAS, LINPACK achieves portability across a wide range of architectures. The BLAS routines allow hardware vendors to optimize the core numerical operations specifically for their machines, which then translates to performance improvements in LINPACK.

The library covers a range of matrix types including general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal matrices. Algorithms are implemented using Gaussian elimination and Cholesky decomposition. LINPACK provides routines for both single-precision and double-precision arithmetic.

LINPACK has been largely superseded by LAPACK (Linear Algebra PACKage), which is a later generation library that offers improved performance, extended functionality, and is written in Fortran 90. LAPACK incorporates block algorithms designed to take advantage of cache memory hierarchies, making it significantly faster on modern architectures than LINPACK. While LINPACK is still functional, it is primarily of historical interest, demonstrating the early development of high-performance numerical linear algebra software. Its influence on subsequent linear algebra libraries and the development of the BLAS standard is significant.