Parallel Implementation of Bisection for the Calculation of Eigenvalues of Tridiagonal Diagonal Symmetric Matrices (Classic Reprint) (Paperback)

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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