Elsevier

Parallel Computing

Volume 6, Issue 3, March 1988, Pages 297-311
Parallel Computing

A parallel Householder tridiagonalization stratagem using scattered square decomposition

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Abstract

The parallel stratagem in this paper uses scattered square decomposition, introduced by G. Fox, for its data assignment and then exploits parallelism in the solution steps of the sequential Householder tridiagonalization algorithm. One may condense a real symmetric full matrix A of order n into a tridiagonal form by the stratagem in concurrent machines where N(= D2) processors are used. Expressions for efficiency and speedup are given for the evaluation of the stratagem. An alternative stratagem which requires less data transmission but more computations is also discussed. The results shown that the Householder Method of tridiagonalization may be implemented on a concurrent machine efficiently by scattered square decomposition provided that the number of matrix elements contained in each processor is much larger than the number of processors of the concurrent machine, and the ratio of the time to transmit one data item from one processor to any other processor to the time to perform a floating-point arithmetic operation is small enough.

Keywords

Linear algebra
tridiagonalizing a symmetric matrix
scattered square decomposition
parallel tridiagonalization stratagem
efficiency analysis

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This paper presents one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract NAS7-100 sponsored by NASA.