Highly Parallel, High-Precision Numerical Integration

Borwein, Jonathan M. and Bailey, David H. (2009) Highly Parallel, High-Precision Numerical Integration. International Journal of Computational Science and Engineering, 4 .

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    This paper describes a scheme for rapidly computing numerical values of definite integrals to very high accuracy, ranging from ordinary machine precision to hundreds or thousands of digits, even for functions with singularities or infinite derivatives at endpoints. Such a scheme is of interest not only in computational physics and computational chemistry, but also in experimental mathematics, where high-precision numerical values of definite integrals can be used to numerically discover new identities. This paper discusses techniques for a parallel implementation of this scheme, then presents performance results for 1-D and 2-D test suites. Results are also given for a certain problem from mathematical physics, which features a difficult singularity, confirming a conjecture to 20,000 digit accuracy. The performance rate for this latter calculation on 1024 CPUs is 690 Gflop/s. We believe that this and one other 20,000-digit integral evaluation that we report are the highest-precision non-trivial numerical integrations performed to date.

    Item Type: Article
    Additional Information: pubdom TRUE
    Subjects: 68-xx Computer science > 68Uxx Computing methodologies and applications
    65-xx Numerical analysis
    28-xx Measure and integration
    Faculty: UNSPECIFIED
    Depositing User: Users 1 not found.
    Date Deposited: 11 May 2005
    Last Modified: 05 Jan 2015 16:01

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