LAPACK Working Note UT CS Parallel numerical linear algebra

We survey general techniques and open problems in numerical lin ear algebra on parallel architectures We rst discuss basic principles of parallel processing describing the costs of basic operations on parallel ma chines including general principles for constructing e cient algorithms We illustrate these principles using current architectures and software systems and by showing how one would implement matrix multiplica tion Then we present direct and iterative algorithms for solving linear systems of equations linear least squares problems the symmetric eigen value problem the nonsymmetric eigenvalue problem and the singular value decomposition We consider dense band and sparse matrices