Generalized averaged Szegő quadrature rules

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• 作者：Carl Jagels^a ; ^{jagels@hanover.edu" class="auth_mail" title="E-mail the corresponding author} ; Lothar Reichel^b ; ^{reichel@math.kent.edu" class="auth_mail" title="E-mail the corresponding author} ; Tunan Tang^b ; ^{nickdon2006@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Szegő quadrature ; Error estimation ; Periodic functions ; Generalized averaged Gauss quadrature
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：311
• 期：Complete
• 页码：645-654
• 全文大小：469 K

文摘

Szegő quadrature rules are commonly applied to integrate periodic functions on the unit circle in the complex plane. However, often it is difficult to determine the quadrature error. Recently, Spalević introduced generalized averaged Gauss quadrature rules for estimating the quadrature error obtained when applying Gauss quadrature over an interval on the real axis. We describe analogous quadrature rules for the unit circle that often yield higher accuracy than Szegő rules using the same moment information and may be used to estimate the error in Szegő quadrature rules.