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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. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com 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.

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