Gaussian Quadrature in the Complex Plane

Paul Saylor
Dept. of Computer Science
University of Illinois, Urbana-Champaign
Urbana, IL 61801

Dennis C. Smolarski, S.J.
Dept. of Mathematics
Santa Clara University
Santa Clara, CA 95053-0290

Gene Golub with a number of co-authors has connected Gaussian quadrature with many fundamental estimates in iterative methods, usually related to inner products. However, in estimating inner products arising from the Bi-Conjugate Gradient (BCG) method, an extension already made, classical Gaussian Quadrature does not apply. In this talk, we fill in the background needed to follow recent Gaussian quadrature-based estimates of certain inner products associated with BCG. See Estimating the Received Signal II, this conference.

Gaussian quadrature, Bi-Conjugate Gradient Method, inner products