Related Work

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Next: Dense Linear Algebra Up: Templates for Linear Algebra Previous: Introduction and Motivation

Related Work


Many excellent numerical linear algebra texts [33][11][30][25][43] and black-box software libraries [1][24][36] already exist. A great deal of more specialized software for eigenproblems also exists, for example, for surveys on the subject see [4][31].

A book of templates, including software, has already been written for iterative methods for solving linear systems [6], although it does not include all the ingredients mentioned above. In particular, it discusses some important advanced methods, such as preconditioning, domain decomposition and multigrid, relatively briefly, and does not have a comprehensive set of numerical examples to help explain the expected performance from each algorithm on various problem classes. It has a relatively simple decision tree to help users choose an algorithm. Nevertheless, it successfully incorporates many of the features we wish to have.

The linear algebra chapter in Numerical Recipes [32] contains a brief description of the conjugate gradient algorithm for sparse linear systems and the eigensystem chapter only contains the basic method for solving dense standard eigenvalue problem, all of the methods and available software in the recipes, except the Jacobi method for symmetric eigenvalue problem, are simplified version of algorithms in the EISPACK and LAPACK. Beside on disk, the software in the recipes are actually printed line by line in the book.

Jack Dongarra
Wed Jun 21 02:35:11 EDT 1995