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Analysis of Asynchronous Polynomial Root Finding Methods on a Distributed Memory Multicomputer
June 1994 (vol. 5 no. 6)
pp. 639-648

We have studied various implementations of iterative polynomial root finding methods on a distributed memory multicomputer. These methods are based on the construction of a sequence of approximations that converge to the set of zeros. The synchronous version consists in sharing the computation of the next iterate among the processors and updating their data through a total exchange of their results. In order to decrease thecommunication cost, we introduce asynchronous versions. The computation of the nextiterate is still shared among the processor, but the updating is done by using only nearestneighbor communications. We prove that under weak conditions, these asynchronousversions are still locally convergent, even if their convergence orders are reduced. Weanalyze the behavior of the asynchronous methods in function of their delay, thetopology of the interconnection network, and the elementary computation andcommunication times. We have implemented and compared these methods on ahypercube multicomputer.

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Index Terms:
Index Termsconvergence of numerical methods; poles and zeros; polynomials; distributed memorysystems; asynchronous polynomial root finding; distributed memory multicomputer;iterative polynomial root finding; synchronous; locally convergent; convergence;hypercube multicomputer; polynomial zeros; asynchronous methods
M. Cosnard, P. Fraigniaud, "Analysis of Asynchronous Polynomial Root Finding Methods on a Distributed Memory Multicomputer," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 6, pp. 639-648, June 1994, doi:10.1109/71.285609
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