Parallel Two-Stage Reduction of a Regular Matrix Pair to Hessenberg-Triangular Form

@inproceedings{Adlerborn2000ParallelTR,
title={Parallel Two-Stage Reduction of a Regular Matrix Pair to Hessenberg-Triangular Form},
author={Bj{\"o}rn Adlerborn and Krister Dackland and Bo K{\aa}gstr{\"o}m},
booktitle={PARA},
year={2000}
}
• Published in PARA 18 June 2000
• Computer Science
A parallel two-stage algorithm for reduction of a regular matrix pair (A,B) to Hessenberg-triangular form (H, T) is presented. Stage one reduces the matrix pair to a block upper Hessenberg-triangular form (Hr, T), where Hr is upper r-Hessenberg with r > 1 subdiagonals and T is upper triangular. In stage two, the desired upper Hessenberg-triangular form is computed using two-sided Givens rotations. Performance results for the ScaLAPACK-style implementations show that the parallel algorithms can…

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References

SHOWING 1-10 OF 16 REFERENCES

Reduction of a Regular Matrix Pair (A, B) to Block Hessenberg Triangular Form

• Mathematics
PARA
• 1995
It is shown how an elementwise algorithm can be reorganized in terms of blocked factorizations and higher level BLAS operations, and several ways to annihilate elements are compared.

A ScaLAPACK-Style Algorithm for Reducing a Regular Matrix Pair to Block Hessenberg-Triangular Form

• Computer Science
PARA
• 1998
It is shown how a sequential elementwise algorithm can be reorganized in terms of blocked factorizations and matrix-matrix operations to form a parallel algorithm for reduction of a regular matrix pair to block Hessenberg-triangular form.

Blocked algorithms and software for reduction of a regular matrix pair to generalized Schur form

• Computer Science
TOMS
• 1999
A two-stage blocked algorithm for reduction of a regular matrix pair (<italic>A , B </italic>) to upper Hessenberg-triangular form is presented and a blocked variant of the single-diagonal double-shift QZ method for computing the generalized Schur form of (<itali>A, B</italic>, which outperforms the current LAPACK routines by a factor 2-5 for sufficiently large problems.

A note on the efficient solution of matrix pencil systems

• Computer Science
• 1978
Algorithms for solving matrix pencil systems of linear equations, of the form (A+γB)x=c+γd, are developed and analysed and numerical results are presented which demonstrate the advantages of the new techniques.

An Algorithm for Generalized Matrix Eigenvalue Problems.

• Computer Science
• 1973
A new method, called the $QZ$ algorithm, is presented for the solution of the matrix eigenvalue problem $Ax = \lambda Bx$ with general square matrices A and B. Particular attention is paid to the

A Hierarchical Approach for Performance Analysis of ScaLAPACK-Based Routines Using the Distributed Linear Algebra Machine

• Computer Science
PARA
• 1996
An hierarchical approach for design of performance models for parallel algorithms in linear algebra based on a parallel machine model and the hierarchical structure of the ScaLAPACK library is presented.

LAPACK Users' Guide, Third Edition

• Medicine
Software, Environments and Tools
• 1999

ScaLAPACK Users' Guide

• Education
• 1987
This book is very referred for you because it gives not only the experience but also lesson, it is about this book that will give wellness for all people from many societies.

A Storage-Efficient $WY$ Representation for Products of Householder Transformations

• Computer Science
• 1989
This note describes a storage efficient way to implement the WY representation of Q and shows how the matrix Q can be expressed in the form $Q = I + YTY^{T}$ where $Y \epsilon R^{mxr}$ and \$T Â£ with T upper triangular requires less storage.