The need to evaluate quadrature rules of Gauss-type arises in many applications, and it is often important to assess the accuracy achieved with these rules. Recently, Laurie proposed anti-Gauss quadrature rules, which for many integrands give integration errors of opposite sign as Gauss quadrature rules, and therefore can be used to estimate the error in Gauss quadrature rules. We describe generalizations of anti-Gauss quadrature rules that allow measures with support on the unit circle or in the complex plane. The analysis of, as well as the computation with, these quadrature rules uses the structure of the associated matrices. This talk focuses on exploitation of the structure.
1 Joint work with Daniela CALVETTI and Sun-Mi KIM.