## 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

1 | |

ALGORITHMS APPLICATIONS AND REAL INDUSTRIAL CASES IN ELECTROMAGNETICS | 27 |

ON THE STABLE PARALLEL SOLUTION OF GENERAL NARROW BANDED LINEAR SYSTEMS | 47 |

EIGENVALUE PROBLEMS | 74 |

EFFICIENT ALGORITHMS FOR REDUCING BANDED MATRICES TO BIDIAGONAL AND TRIDIAGONAL FORM | 75 |

PARALLEL BISECTION ALGORITHMS FOR SOLVING THE SYMMETRIC TRIDIAGONAL EIGENPROBLEM | 91 |

A PARALLEL QR ALGORITHM FOR THE SYMMETRIC TRIDIAGONAL EIGENVALUE PROBLEM | 113 |

MATRICES WITH SPECIAL STRUCTURE | 125 |

A NUMERICAL COMPARISON OF LOOKAHEAD LEVINSON AND SCHUR ALGORITHMS FOR NONHERMITIAN TOEPLITZ SYSTEMS | 127 |

SUPERFAST SOLUTION OF LINEAR EQUATIONS WITH LOW DISPLACEMENT RANK | 149 |

PARALLEL COMPUTATION | 162 |

LOADBALANCE IN PARALLEL FACR | 163 |

PARALLEL CGMETHODS AUTOMATICALLY OPTIMIZED FOR PC AND WORKSTATIONCLUSTERS | 181 |

199 | |

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### Common terms and phrases

allocation analysis applied banded linear systems banded matrix bandwidth reduction bidiagonal bisection method BLAS block column blocked transformations cg-method clusters coefficients convergence Cray T3D cyclic reduction denotes displacement rank distributed memory efficient Eigenvalue Problem elements elimination steps elimination with partial fill-in flops Fortran frontal code frontal solver Gaussian elimination GBBRD Householder transformations HSL codes ill-conditioned input inverse iteration LAPACK LDU decomposition Levinson and Schur linear systems load-balance look-ahead Levinson algorithm look-ahead step LU factorization machine Math MRCM nodes nonzero number of processors obtained operations optimization Pade forms parallel algorithm parallel architectures parallel computers parameters partial pivoting partitioning performance permutation phase pstsep QR factorization regular pair reordering rows scalability Schur algorithms Schur complement Section sequential SIAM sine transforms solution solve sparse matrix storage submatrix Subroutine superfast sweep Table technique Toeplitz matrices Toeplitz matrix Toeplitz systems tridiagonal matrix tridiagonal systems unsymmetric update VBAN vector WBRA zero