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Optimizing INTBIS on the CRAY Y-MP

Оптимизация INTBIS для CRAY Y-MP

  • Mathematical Research
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Reliable Computing

Abstract

INTBIS is a well-tested software package which uses an interval Newton/generalized bisection method to find all numerical solutions to nonlinear systems of equations. Since INTBIS uses interval computations, its results are guaranteed to contain all solutions. To efficiently solve very large nonlinear systems on a parallel vector computer, it is necessary to effectively utilize the architectural features of the machine In this paper, we report our implementations of INTBIS for large nonlinear systems on the Cray Y-MP supercomputer. We first present the direct implementation of INTBIS on a Cray. Then, we report our work on optimizing INTBIS on the Cray Y-MP

Abstract

INTBIS—грошедший ушательное тестирование пакет программного обеспения, использюшй интервальный метод Ньютона и обобшенный метод половинного деления гля нахождения всех численных решений систем нелинейных уравнений. Благодаря тому что INTBIS использует интервальные вычисления, получаемые им результаты гарантированно содержат все решения. Для эффективного решения очень больших нелинейных систем на параллельном векторном компьюотере необходимо максимально использобать особенности архитектуры машины. В настояшэй работе описаны реализации INTBIS для больших нелинейных систем на суперкомпьютере Сгау Y-MP Сначала представлена прямая реализация INTBIS для комппьгеров Сгау, а затем излагаются результаты работы по оптимизации INTBIS для Сгау Y-MP

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Authors and Affiliations

  1. Department of Computer and Mathematical Sciences, University of Houston-Downtown, 77002, Houston, Texas, USA

    Chenyi Hu & Joe Sheldon

  2. Department of Mathematics, University of Southwestern Louisiana, U.S.L. Box 4-1010, 70504-1010, Lafayette, LA, USA

    R. Baker Kearfott

  3. Department of Electrical and Computer Engineering, University of Rhode Island, 02881, Kingston, Rhode Island, USA

    Qing Yang

Authors
  1. Chenyi Hu
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  2. Joe Sheldon
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  3. R. Baker Kearfott
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  4. Qing Yang
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Additional information

This research was partially supported by NSF Grants No. DMS-9205680 and No. MIP-9208041

This co-author is a NASA supported undergraduate research assistant at the University of Houston-Downtown. Throughout the paper we will use boldface letters and capital letters to denote interval quantities and vectors, respectively We use\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{x} \) and\(\bar x\) to denote the lower bound and the upper bound for an interval variable x, respectively

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Hu, C., Sheldon, J., Baker Kearfott, R. et al. Optimizing INTBIS on the CRAY Y-MP. Reliable Comput 1, 265–274 (1995). https://doi.org/10.1007/BF02385257

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  • DOI: https://doi.org/10.1007/BF02385257

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