Southern Methodist University
From QUADL to QUADGK
10:10 AM, Thursday, Sept. 3
The main difference between QUADL and QUAD, the original quadrature program of MATLAB, is a pair of formulas of higher degree of precision. The new QUADGK uses a pair of still higher degree, but there are also
important differences in algorithms and capabilities. Vectorization is so important to efficient computation in MATLAB that all its quadrature programs require that evaluation of the integrand be vectorized. The adaptive quadrature codes QUAD and QUADL process a collection of subintervals one at a time, but QUADGK processes them simultaneously-- vectorizing a much larger part of the computation greatly reduces the run time in MATLAB. QUADGK uses algebraic transformations to make it easy to approximate an integral on an infinite interval and to deal with an integrand that has moderate end point singularities. Peano kernels are used to study the accuracy of formulas of high degree of precision and the quality of error estimates when the integrand is of limited differentiability. The pair of QUADGK is seen to be more effective than the pairs of QUAD and QUADL.