ERROR BOUNDS FOR THE NUMERICAL INTEGRATION OF FUNCTIONS WITH LIMITED SMOOTHNESS

ERROR BOUNDS FOR THE NUMERICAL INTEGRATION OF FUNCTIONS WITH LIMITED SMOOTHNESS

Recently, Trefethen (SIAM Rev., 50 (2008), pp. 67–87) and Xiang and Bornemann (SIAM J. Numer. Anal., 50 (2012), pp. 2581–2587) investigated error bounds for n-point Gauss and Clenshaw–Curtis quadrature for the Legendre weight with integrands having limited smoothness properties. Putting their result...

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Veröffentlicht in:SIAM journal on numerical analysis 2014-01, Vol.52 (2), p.877-879
1. Verfasser: DIETHELM, KAI
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Computational mathematics
Error analysis
Error bounds
Errors
Gaussian quadratures
Integrands
Mathematical analysis
Mathematical functions
Mathematical models
Mathematical theorems
Numerical analysis
Numerical integration
Numerical quadratures
Polynomials
Quadratures
Smoothness
Weight function
Weighting functions
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Beschreibung
Zusammenfassung:Recently, Trefethen (SIAM Rev., 50 (2008), pp. 67–87) and Xiang and Bornemann (SIAM J. Numer. Anal., 50 (2012), pp. 2581–2587) investigated error bounds for n-point Gauss and Clenshaw–Curtis quadrature for the Legendre weight with integrands having limited smoothness properties. Putting their results into the context of classical quadrature theory, we find that the observed behavior is by no means surprising and that it can essentially be proved for a very large class of quadrature formulas with respect to a broad set of weight functions.
ISSN:0036-1429
1095-7170
DOI:10.1137/130921246