Publication: INTE: A UNIVAC 1108/1110 Program for Numerical Integration with Rigorous Error Estimation
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INTE: A UNIVAC 1108/1110 Program for Numerical Integration with Rigorous Error Estimation

- Technical report -
 

Author(s)
Julia H. Gray , Louis B. Rall

Institution
Mathematics Research Center, University of Wisconsin - Madison

Year
1975

Abstract
The application of the Euler-Maclaurin formula for numerical integration can be automated by using software for interval analysis and differentiation arithmetic. The interval techniques permit rigorous bounding of the error due to roundoff, and also the truncation error. Optimal results for these bounds are developed to give a required accuracy in minimum time, or an estimate of the ultimate accuracy obtained using a UNIVAC 1108/1110 program. (Paper abstract).

BibTeX
@TECHREPORT{
         Gray1975IAU,
       AUTHOR = "Julia H. Gray and Louis B. Rall",
       TITLE = "{INTE}: {A} {UNIVAC} 1108/1110 Program for Numerical Integration with Rigorous Error
         Estimation",
       INSTITUTION = "Mathematics Research Center, University of Wisconsin - Madison",
       YEAR = "1975",
       TYPE = "MRC Technical Summary Report",
       NUMBER = "No. 1428",
       REFERRED = "[Rall1996AIt].",
       KEYWORDS = "interval algorithm; Euler-Maclaurin quadrature; differentiation arithmetic;
         computer program; error estimation.",
       ABSTRACT = "The application of the Euler-Maclaurin formula for numerical integration can be
         automated by using software for interval analysis and differentiation arithmetic. The interval
         techniques permit rigorous bounding of the error due to roundoff, and also the truncation error.
         Optimal results for these bounds are developed to give a required accuracy in minimum time, or an
         estimate of the ultimate accuracy obtained using a UNIVAC 1108/1110 program. (Paper abstract)."
}


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