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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.
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