Summary
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.
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References
Rice, J. R.: A metalgorithm for adaptive quadrature. J. ACM. 22, 61–82 (1975)
Rice, J. R.: Parallel algorithms for adaptive quadrature — Convergence. Proc. IFIP Congress 74, Stockholm. Amsterdam: North-Holland 1974, p. 600–604
Rice, J. R.: Parallel algorithms for adaptive quadrature III — Program Correctness, ACM Trans. Math. Software, 2 (1976) to appear
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Rice, J.R. Parallel algorithms for adaptive quadrature II metalgorithm correctness. Acta Informatica 5, 273–285 (1975). https://doi.org/10.1007/BF00264562
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DOI: https://doi.org/10.1007/BF00264562