Abstract
This study is concerned with parallel algorithms for the orthogonal reduction of a general matrix to upper Hessenberg form. A variety of algorithms are investigated, which involve varying amounts of overlap between different parts of the calculation. Empirical comparison was carried out using C++ and the THREADS package on a shared memory Encore Multimax multiprocessor. In this testing the final version which involves most overlap was found to be the most efficient algorithm, and its efficiency is very high. The algorithms illustrate the advantages of parallel algorithms using dynamic allocation of tasks to THREADs on this shared memory machine.
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