NDLI: Rates of Convergence of Gaussian Quadrature for Singular Integrands

Content Provider	Scilit
Author	Lubinsky, D. S. Rabinowitz, P.
Copyright Year	1984
Description	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.
Related Links	https://www.ams.org/mcom/1984-43-167/S0025-5718-1984-0744932-2/S0025-5718-1984-0744932-2.pdf
Ending Page	242
Page Count	24
Starting Page	219
ISSN	00255718
e-ISSN	10886842
DOI	10.2307/2007407
Journal	Mathematics of Computation
Issue Number	167
Volume Number	43
Language	English
Publisher	Duke University Press
Publisher Date	1984-07-01
Access Restriction	Open
Subject Keyword	Mathematical Physics Functions Singularity Convergence Gaussian Quadrature Ignore Integrands Respect Algebraic
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Algebra and Number Theory Computational Mathematics

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