Rates of convergence of Gaussian quadrature for singular integrands

Authors:
D. S. Lubinsky and P. Rabinowitz

Journal:
Math. Comp. **43** (1984), 219-242

MSC:
Primary 65D30

DOI:
https://doi.org/10.1090/S0025-5718-1984-0744932-2

MathSciNet review:
744932

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Abstract: The authors obtain the rates of convergence (or divergence) of Gaussian quadrature on functions with an algebraic or logarithmic singularity inside, or at an endpoint of, the interval of integration. A typical result is the following: For a bounded smooth weight function on , the error in *n*-point Gaussian quadrature of is if and if , provided we avoid the singularity. If we ignore the singularity *y*, the error is for almost all choices of *y*. These assertions are sharp with respect to order.

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DOI:
https://doi.org/10.1090/S0025-5718-1984-0744932-2

Article copyright:
© Copyright 1984
American Mathematical Society