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

  • V. Fragnelli
  • Giovanni Resta
Part of the Applied Information Technology book series (AITE)


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.


Computational Complexity Parallel Architecture Super Computer Float Point Operation Efficient Data Structure 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    G. Resta, An algorithm for the least squares solution of suitably structured linear systems. To appear.Google Scholar
  2. [2]
    P.E. Gill, W. Murray, Numerical methods for constrained optimization. Academic Press, (1974).Google Scholar
  3. [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.Google Scholar
  4. [4]
    L. Galli, G. Resta, Implementation of a data-flow algorithm for linear programming. Parallel Computing 83, Feilmeier, Joubert and Schendel, editors, Elsevier (1984).Google Scholar
  5. [5]
    G. Resta, The binary cube: a superstructure for super computers, Numerical Optimisation Centre T.R. 144, Hatfield Pol technic (U.K.), (1984).Google Scholar

Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • V. Fragnelli
    • 1
  • Giovanni Resta
    • 1
  1. 1.Mathematical InstituteUniversity of GenovaItaly

Personalised recommendations