Useful linear algebra references
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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.
Page created and maintained by Brendan McMahan, last modified 9/14/2004.