Academic Commons

Reports

Is Gauss quadrature optimal for analytic functions?

Kowalski, M. A.; Werschulz, Arthur G.; Wozniakowski, Henryk

We consider the problem of optimal quadratures for integrands f: [ -1 , 1 ] → R which have an analytic extension f to an open disk D, of radius r about the origin such that |f| ≤ 1 on Dr. If r = 1, we show that the penalty for sampling the integrand at zeros of the Legendre polynomial of degree n rather than at optimal points, tends to infinity with n. In particular there is an "infinite" penalty for using Gauss quadrature. On the other hand, if r > l, Gauss quadrature is almost optimal. These results hold for both the worst-case and asymptotic settings.

Files

More About This Work

Academic Units
Computer Science
Publisher
Department of Computer Science, Columbia University
Series
Columbia University Computer Science Technical Reports, CUCS-081-83
Published Here
October 26, 2011
Academic Commons provides global access to research and scholarship produced at Columbia University, Barnard College, Teachers College, Union Theological Seminary and Jewish Theological Seminary. Academic Commons is managed by the Columbia University Libraries.