Sparse 1.3, authored by Ken Kundert, was developed around 1985 in Berkeley. It is the direct linear solver for the Spice simulator. Visit the official website for more information: http://www.netlib.org/sparse/ . The source code is in C.
SuperLU was developed by a group of computer scientists in Berkeley, Xerox Palo Alto Research Center, and National Energy Research Scientific Computing (NERSC) Center around 1995. There different versions of source code can be downloaded from http://www.nersc.gov/~xiaoye/SuperLU/ . SuperLU implements the supernode concepts. The weakness of SuperLU is that it relies on good ordering provided by other packages. The linked gz file is the sequential version with the Makefile corrected for local use. Also, a serious bug in the source code: SRC/sp_coletree.c (function void etdfs(int v)) was corrected. The original code uses recusioin that could cause stack overflow when the matrix size exceeds some limit.
hypre is a software library for solving large, sparse linear systems of equations on massively parallel computers. The library was created with the primary goal of providing users with advanced parallel preconditioners. hypre was created by Lawrence Livermore National Laboratory, Center for Applied Scientific Computing. The package has been successfully built on single processor UNIX box by using MPI. For more information, visit http://acts.nersc.gov/hypre/ . For a quick browse, read the manuals: User's Manual and hypre Reference Manual .
Developed by R.S. Tuminaro et al at Sandia National Lab. Aztec is an iterative solver library, designed for parallel solution of Ax = b . The package was specifically designed for numerical solution of PDEs. Aztec includes Krylov iterative methods such Conjugate Gradient (CG), Generalized Minimum Residual (GMRES), and Stabilized Biconjugate Gradient (BiCGSTAB). These Krylov methods are used with various preconditioners such as polynomial, domain decomposition methods using LU, and Incomplete LU (ILU) factorization within subdomains . For more information, visit http://acts.nersc.gov/aztec/ . Aztec can be compiled without MPI.
DASSL was developed by Prof. Linda R. Petzold around 1983 when she was in Lawrence Livermore Nat'l Lab. It was written in Fortran and used widely. It guarantees to solve index 0 and 1 DAEs. DASSL approximates the derivative using the kth order BDF, 0 £ k £ 5. At every step it chooses the order k and the step size based on the behavior of the solution. More specifically, it uses a variable step size, variable order, fixed leading coefficient implementation of BDF. Visit DASSL .