Summary
The Jacobi Overrelaxation (JOR) method is usually cited as a “perfect” parallel algorithm, whereas the Successive Overrelaxation (SOR) method is considered as quite the opposite. For linear systems with dense matrices, an algorithm for the SOR method is presented which is suited for parallelization nearly in the same way as JOR. For systems with band matrices, an algorithm is described which, using a pipeline principle, yields a speedupS=p(1+(p−1)p/m) −1, wherep denotes the number of processors andm the number of SOR iterations. Thus form=p, there is no speedup whereas the speedup tends to its maximal valuep ifm tends to infinity.
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Dedicated to the memory of Peter Henrici
Research supported by the Air Force Office of Scientific Research
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Niethammer, W. The SOR method on parallel computers. Numer. Math. 56, 247–254 (1989). https://doi.org/10.1007/BF01409787
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DOI: https://doi.org/10.1007/BF01409787