🚀 go-pugleaf

           Department of Computer Science, University of Toronto
         (SF = Sandford Fleming Building, 10 King's College Road)

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                            NUMERICAL ANALYSIS
                   SF1105, at 11:00 a.m., 6 October 1992

                                P. W. Sharp
              Mathematics and Statistics, Queen's University

                                 Abstract

In the last twenty years, many automatic routines have been developed for
the numerical evaluation of one-dimensional definite integrals.  These
routines attempt to find an approximation to the integral that differs from
the true value by less than an amount specified by the user.

The preponderance of automatic routines has naturally led to the idea of
testing routines to see which ones are suitable for different types of
integrals. Two contrasting testing paradigms have been used: battery
testing and parameter testing. Battery testing involves measuring the
performance of the routines on a collection of integrals which display a
variety of properties. Parameter testing involves measuring the performance
on a family of similar integrals.

I will begin with a review of manual and automatic quadrature routines.
Then I will discuss the two testing paradigms and present a general view
that contains the paradigms as special cases. Next, I will describe Q1STAT,
a testing package I have developed. In the final part of the talk, I will
illustrate the use of Q1STAT.