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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



On the remainder of Gaussian quadrature formulas for Bernstein-Szegő weight functions

Author: F. Peherstorfer
Journal: Math. Comp. 60 (1993), 317-325
MSC: Primary 65D32
MathSciNet review: 1153169
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Abstract: We give an explicit expression for the kernel of the error functional for Gaussian quadrature formulas with respect to weight functions of Bernstein-Szegö type, i.e., weight functions of the form $ {(1 - x)^\alpha }{(1 + x)^\beta }/\rho (x),\quad x \in ( - 1,1)$, where $ \alpha ,\beta \in \{ - \tfrac{1}{2},\tfrac{1}{2}\} $ and $ \rho $ is a polynomial of arbitrary degree which is positive on $ [ - 1,1]$. With the help of this result the norm of the error functional can easily be calculated explicitly for a wide subclass of these weight functions.

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Article copyright: © Copyright 1993 American Mathematical Society