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The error norm of Gauss-Radau quadrature formulae for Bernstein-Szegö weight functions


Author: Sotirios E. Notaris
Journal: Math. Comp. 84 (2015), 2843-2865
MSC (2010): Primary 65D32
DOI: https://doi.org/10.1090/mcom/2944
Published electronically: April 15, 2015
MathSciNet review: 3378850
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the Gauss-Radau quadrature formulae for the
Bernstein-Szegö weight functions consisting of any one of the four Chebyshev weights divided by the polynomial $ \rho (t)=1-\frac {4\gamma }{(1+\gamma )^{2}}t^{2},\ -1<t<1,\ -1<\gamma \leq 0$. On certain spaces of analytic functions the error term of these formulae is a continuous linear functional. We compute or estimate the norm of the error functional.


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Additional Information

Sotirios E. Notaris
Affiliation: Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Athens, Greece
Email: notaris@math.uoa.gr

DOI: https://doi.org/10.1090/mcom/2944
Keywords: Gauss-Radau quadrature formulae, Bernstein-Szeg\"o weight functions, error norm
Received by editor(s): August 6, 2013
Received by editor(s) in revised form: February 1, 2014
Published electronically: April 15, 2015
Dedicated: Dedicated to Walter Gautschi on his 85th birthday with respect and admiration
Article copyright: © Copyright 2015 American Mathematical Society