A note on Peano constants of Gauss-Kronrod quadrature schemes

For the error R 2 n + 1 GK of the Gauss-Kronrod quadrature formula Q 2 n + 1 GK, we prove the precise asymptotic value of the low-order Peano constants c s ( R 2 n + 1 GK), where s is fixed for increasing n. The result is applied for comparisons of the Gauss-Kronrod formula Q 2 n + 1 GK with the Gau...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 66; no. 1; pp. 177 - 183
Main Author Ehrich, Sven
Format Journal Article Conference Proceeding
LanguageEnglish
Published Amsterdam Elsevier B.V 01.01.1996
Elsevier
Subjects
Error estimates
Exact sciences and technology
Gauss-Kronrod quadrature
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Numerical methods in mathematical programming
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Numerical methods in probability and statistics
Peano constants
Sciences and techniques of general use
Error estimates
Peano constants
65D32
Gauss-Kronrod quadrature
Quadrature
Error estimation
Numerical methods
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Summary:For the error R 2 n + 1 GK of the Gauss-Kronrod quadrature formula Q 2 n + 1 GK, we prove the precise asymptotic value of the low-order Peano constants c s ( R 2 n + 1 GK), where s is fixed for increasing n. The result is applied for comparisons of the Gauss-Kronrod formula Q 2 n + 1 GK with the Gauss formula Q n G and with the Gauss formula Q 2 n + 1 G, with respect to this often used quality measure.
Bibliography:SourceType-Scholarly Journals-2
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ObjectType-Conference Paper-1
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SourceType-Conference Papers & Proceedings-1
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ISSN:0377-0427
1879-1778
DOI:10.1016/0377-0427(95)00173-5