Unsymmetric sparse systems of linear equations

Direct methods

• Sparse numerical linear algebra: direct methods and preconditioning
  Iain. S. Duff. 1997. [PDF], [webpage]
  Comments: Good overview of direct methods up to 1997. Survey level without technical details.


• Recent advances in direct methods for solving unsymmetric sparse systems of linear equations
  Anshul Gupta. [webpage]
  Comments: Survey that analyses the impact of various techniques via numerical experiments. Focuses on the WSMP solver. References to papers with technical details on techniques employed.


• A combined unifrontal/multifrontal method for unsymmetric sparse matrices
  Timothy Davis and Iain S. Duff. 1999. [webpage]
  Comments: Good algorithm, but you may need to read some earlier papers to understand it. Maybe start with the Davis and Duff paper from 1997.


• PARDISO software
  [webpage] Comments: Currently the best package for direct solution of sparse systems (?). Here is a paper


• WSMP software
  [webpage] Comments: Currently one of the best packages.

Iterative methods

• Templates for the solution of linear systems: building blocks for iterative methods
  R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato , J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. Van der Vorst. 1994. [webpage]
  Comments: This book is a comprehensive reference on iterative solutions. Full text is available online in [ps].


• Matrix Toolkits for Java (MTJ) [webpage]
  Comments: Thanks to Matt Rosencrantz for pointing me to this package. It looks to be a full-featured Java matrix package that uses calls to native BLAS and LAPACK libraries. If you like writing in Java (like I do) and need fast matrix routines this might be a good place to start.