The error norm of Gaussian quadrature formulae for weight functions of Bernstein-Szegö type
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- Notaris, S.E. Numer. Math. (1990) 57: 271. doi:10.1007/BF01386411
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We consider the Gaussian quadrature formulae for the Bernstein-Szegö weight functions consisting of any one of the four Chebyshev weights divided by an arbitrary quadratic polynomial that remains positive on [−1, 1]. Using the method in Akrivis (1985), we compute the norm of the error functional of these quadrature formulae. The quality of the bounds for the error functional, that can be obtained in this way, is demonstrated by two numerical examples.