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A parallel complex zero finder

Параллельная процедура поиска комплексных нулей

  • Mathematical Research
  • Published:
Reliable Computing

Abstract

A recent paper [7] describes a variable precision interval arithmetic algorithm for the computation of the zeros of an analytic function inside a given rectangle and to a user-specified accuracy. The algorithm is based on the argument principle in the set of complex numbersC and carries much potential for parallelization at various levels of granularity. Here we explain how to modify the sequential algorithm to take advantage of parallelism at four levels ranging from coarse to medium grain. The algorithm is tested in a distributed environment consisting of eight SPARC workstations. The underlying software environment is also discussed.

Abstract

В недавней работе [7] описан интервально-арифметический алгоритм переменной разрядности для вычисления нулей аналитической функции внутри заданното прямоугольника с точностью, определяемой пользователем. Этот алгоритм основан на принципе аргумента на множестве комплексных чиселС и обладает большим потенциалом параллелизации на пазных уровнях гранулированности. В настокшей работе предлагается модификация последовательного алгоритма с использованием параллелизации на четырех уровнях гранулированности: дт грубого до среднезерхистого. Алгоритм тестировался в распределенной вычислительной сети, состояшей из восьми рабочих станций ЅРА--RС. Опеределенное внимахие уделено программному обеспечению нижнего уровня.

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References

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Authors and Affiliations

  1. Wilhelm-Schickard-Institut, Universität Tübingen, Sand 13, 72076, Tübingen, Germany

    Mark J. Schaefer & Tilmann Bubeck

Authors
  1. Mark J. Schaefer
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  2. Tilmann Bubeck
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Schaefer, M.J., Bubeck, T. A parallel complex zero finder. Reliable Comput 1, 317–323 (1995). https://doi.org/10.1007/BF02385261

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  • DOI: https://doi.org/10.1007/BF02385261

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