Acta Informatica

, Volume 5, Issue 4, pp 273–285 | Cite as

Parallel algorithms for adaptive quadrature II metalgorithm correctness

  • John R. Rice


This paper introduces a rather specific metalgorithm (or meta-program) for a class of algorithms for adaptive quadrature on parallel (MIMD) computers. This class includes all the current approaches to adaptive quadrature. The main result is that any member of this metalgorithm satisfies the conditions of a traditional numerical analysis convergence theorem from [2]. The algorithm structure in this metalgorithm is specified in some detail and 32 Attributes are assumed. These Attributes and structure serve to guide the design of particular algorithms. They also facilitate establishing algorithm correctness by providing a detailed set of algorithm properties (most of which are like “assertions” in program proving) that are sufficient for correctness.


Information System Operating System Data Structure Communication Network Information Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Rice, J. R.: A metalgorithm for adaptive quadrature. J. ACM. 22, 61–82 (1975)Google Scholar
  2. 2.
    Rice, J. R.: Parallel algorithms for adaptive quadrature — Convergence. Proc. IFIP Congress 74, Stockholm. Amsterdam: North-Holland 1974, p. 600–604Google Scholar
  3. 3.
    Rice, J. R.: Parallel algorithms for adaptive quadrature III — Program Correctness, ACM Trans. Math. Software, 2 (1976) to appearGoogle Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • John R. Rice
    • 1
  1. 1.Division of Mathematical SciencesPurdue UniversityWest LafayetteUSA

Personalised recommendations