## High Performance Algorithms for Structured Matrix ProblemsThe main aim of this volume is to summarise the state of the art in the area of high performance solutions of structured linear systems as well as the area of structured eigenvalue and singular-value problems. The volume highlights research directions perceived to be the most important for computing the structured problems. The topics covered range from parallel solvers for sparse or banded linear systems to parallel computation of eigenvalues and singular values of tridiagonal and bidiagonal matrices. In addition, the volume contains articles on specialised solution techniques for dense Toeplitz and Hankel matrices. The papers also discuss implementation issues on numerous parallel architectures such as vector computers, shared and distributed memory multiprocessors, and clusters of workstations. |

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### Contents

A Comparison of Frontal Software with other Harwell Subroutine | 1 |

Algorithms Applications | 27 |

On the Stable Parallel Solution of General Narrow Banded | 47 |

Copyright | |

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### Common terms and phrases

analysis applied banded matrix bidiagonal bisection method bit-reversed BLAS block column block LDU decomposition blocked transformations cg-method classical algorithms clusters coefficients column-regular communication structure convergence CRAY Cray T3D cyclic allocation denotes diagonal displacement rank displacement representation efficient elimination steps flops Fortran frontal solver Gaussian elimination Householder transformations ill-conditioned implementation input INTEGER iteration LAPACK Levinson and Schur Linear Algebra linear systems load-balance look-ahead algorithms look-ahead Levinson algorithm look-ahead step machine Math nodes number of processors obtained operations optimization overhead parallel algorithms parallel computers parameters partial pivoting partitioning performance permutation phase Poisson's equation QR factorization recurrences regular pair rows scalability Schur algorithm Schur complement Section sequential SIAM sine transforms solution solvers solving sparse sparse matrix speedup subroutines symmetric positive definite symmetric tridiagonal Table Tabu technique Theorem Toeplitz matrix Toeplitz systems tridiagonal matrices tridiagonal matrix tridiagonal systems update values WBRA zero