Stopping functionals for Gaussian quadrature formulas

Gaussian formulas are among the most often used quadrature formulas in practice. In this survey, an overview is given on stopping functionals for Gaussian formulas which are of the same type as quadrature formulas, i.e., linear combinations of function evaluations. In particular, methods based on ex...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 127; no. 1; pp. 153 - 171
Main Author Ehrich, Sven
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.01.2001
Subjects
Error estimates
Gaussian quadrature formulas
Gauss–Kronrod formulas
Stopping functionals
Error estimates
Gauss–Kronrod formulas
Gaussian quadrature formulas
Stopping functionals
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Summary:Gaussian formulas are among the most often used quadrature formulas in practice. In this survey, an overview is given on stopping functionals for Gaussian formulas which are of the same type as quadrature formulas, i.e., linear combinations of function evaluations. In particular, methods based on extended formulas like the important Gauss–Kronrod and Patterson schemes, and methods which are based on Gaussian nodes, are presented and compared.
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(00)00496-9