Rates of convergence of Gaussian quadrature for singular integrands
Authors:
D. S. Lubinsky and P. Rabinowitz
Journal:
Math. Comp. 43 (1984), 219242
MSC:
Primary 65D30
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 npoint 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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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198407449322
PII:
S 00255718(1984)07449322
Article copyright:
© Copyright 1984 American Mathematical Society
