On the remainder of Gaussian quadrature formulas for Bernstein-Szegő weight functions
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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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Math. Comp. 60 (1993), 317-325
- MSC: Primary 65D32
- DOI: https://doi.org/10.1090/S0025-5718-1993-1153169-2
- MathSciNet review: 1153169