INTE: A UNIVAC 1108/1110 Program for Numerical Integration with Rigorous Error Estimation.
Abstract
By use of the concepts of interval analysis, one can construct methods for numerical integration which give rigorous bounds on errors due to imprecise data, round-off, and truncation, and also make possible the detection of the use of incorrect formulas. On the basis of parameters obtained from interval integration formulas, the calculation of numerical integrals can be optimized with respect to time and accuracy. Improved error bounds can also be obtained in certain cases by intersection of interval results. This paper describes a computational system of interval type which has been implemented as a computer program for the UNIVAC 1108/1110, using software previously developed at MRC for interval analysis and automatic differentiation. The program accepts integrands which are functions of a single variable, written as one or more ordinary FORTRAN statements. In addition to the variable of integration, these statements may include one or more parameters to be specified by the user, and the program may be used in interactive or batch mode.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1975
- Accession Number
- ADA020197
Entities
People
- Julia H. Gray
- Louis B. Rall
Organizations
- University of Wisconsin–Madison