Parallel Implementation of Bisection for the Calculation of Eigenvalues of

Herbert J. Bernstein, Max Goldstein

ISBN 10: 1332175619 / ISBN 13: 9781332175611

Edité par Forgotten Books, 2018

A propos de cet article

Print on Demand. This book delves into the application of bisection for the computation of eigenvalues. The technique of bisection is a widely recognized numerical approach commonly used for approximating the roots of nonlinear equations. The author meticulously investigates how bisection can be effectively applied to determine the eigenvalues of a symmetric tridiagonal matrix. By exploring both sequential and parallel implementations of the bisection algorithm, the author provides valuable insights into the method's accuracy and efficiency. The book offers a comprehensive examination of the bisection method, making it an invaluable resource for researchers and practitioners seeking a deeper understanding of eigenvalue computation techniques. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.

N° de réf. du vendeur 9781332175611_0

Détails bibliographiques

• Titre: Parallel Implementation of Bisection for the Calculation of Eigenvalues of
• Éditeur: Forgotten Books
• Date de parution: 2018
• Langue: anglais
• ISBN à 10 chiffres: 1332175619
• ISBN à 13 chiffres: 9781332175611
• Reliure: Paperback
• État de l'article: New
• Type de livre: print-on-demand item
• Catalogues du vendeur:
  • Calculus

A propos de ce titre

Synopsis

Excerpt from Parallel Implementation of Bisection for the Calculation of Eigenvalues of Tridiagonal Diagonal Symmetric Matrices

1. Introduction

Kuck and Sameh [9] noted that completion of a Givens or Householder eigenvalue algorithm on a parallel machine may be done by a parallel implementation of a bisection algorithm. In this paper we investigate the considerations involved in the implementation of this idea on an MIMD (multiple instruction stream - multiple data stream) machine with a smaller number of processors available than eigenvalues to be found.

There are three major alternatives to consider:

1. Convert the serial Sturm sequence code to a parallel algorithm.
2. For each interval compute more than one division point in parallel.
3. Process more than one interval at a time.

We will show that the last alternative has certain advantages for MIMD machines.

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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.