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An ABS Method for Solving Suitably Structured Linear Systems is Supported by Parallel Architectures

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Parallel Processing Techniques for Simulation

Part of the book series: Applied Information Technology ((AITE))

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Summary

We present an algorithm based on a method belonging to the class of Abaffy-Broyden-Spedicato [3]. The linear system to be solved can be sparse and in this situation must have a row-polychromatic structure.

Suggestions are given in order to exploit the high degree of freedom of the class, A suitable data structure reduces computation and memory requirements. The computations specified by the algorithm have a high degree of parallelism.

The computational complexity of the algorithm is discussed. Parallel architectures supporting the algorithm are examined.

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References

  1. G. Resta, An algorithm for the least squares solution of suitably structured linear systems. To appear.

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  2. P.E. Gill, W. Murray, Numerical methods for constrained optimization. Academic Press, (1974).

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  3. J. Abaffy, S. Broyden, E. Spedicato, A class of methods for linear equations II: Non-singular representation, parameter solution and other tales. Report IAM1.

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  4. L. Galli, G. Resta, Implementation of a data-flow algorithm for linear programming. Parallel Computing 83, Feilmeier, Joubert and Schendel, editors, Elsevier (1984).

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  5. G. Resta, The binary cube: a superstructure for super computers, Numerical Optimisation Centre T.R. 144, Hatfield Pol technic (U.K.), (1984).

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Author information

Authors and Affiliations

  1. Mathematical Institute, University of Genova, Italy

    V. Fragnelli & Giovanni Resta

Authors
  1. V. Fragnelli
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  2. Giovanni Resta
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Editor information

Editors and Affiliations

  1. UMIST, Manchester, England

    M. G. Singh

  2. Imperial Chemical Industries PLC, Northwich, Cheshire, England

    A. Y. Allidina

  3. National Computing Centre Ltd., Manchester, England

    B. K. Daniels

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© 1986 Plenum Press, New York

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Fragnelli, V., Resta, G. (1986). An ABS Method for Solving Suitably Structured Linear Systems is Supported by Parallel Architectures. In: Singh, M.G., Allidina, A.Y., Daniels, B.K. (eds) Parallel Processing Techniques for Simulation. Applied Information Technology. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5218-1_7

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  • DOI: https://doi.org/10.1007/978-1-4684-5218-1_7

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-5220-4

  • Online ISBN: 978-1-4684-5218-1

  • eBook Packages: Springer Book Archive

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