The error norm of Clenshaw–Curtis and related quadrature formulae
| Autor: | Sotirios E. Notaris |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Quadrature domains
Computer Networks and Communications Applied Mathematics Mathematical analysis 010103 numerical & computational mathematics 01 natural sciences Gauss–Kronrod quadrature formula Tanh-sinh quadrature Mathematics::Numerical Analysis Quadrature (mathematics) 010101 applied mathematics Computational Mathematics Gauss–Jacobi quadrature Applied mathematics 0101 mathematics Legendre polynomials Software Gauss–Hermite quadrature Clenshaw–Curtis quadrature Mathematics |
| Zdroj: | BIT Numerical Mathematics. 56:705-728 |
| ISSN: | 1572-9125 0006-3835 |
| DOI: | 10.1007/s10543-015-0569-6 |
| Popis: | We consider interpolatory quadrature formulae relative to the Legendre weight function $$w(t)=1$$ on the interval $$[-1,1]$$ . On certain spaces of analytic functions the error term of these formulae is a continuous linear functional. We obtain new estimates for the norm of the error functional when the latter does not keep a constant sign at the monomials. Subsequently, the derived estimates are applied into the case of the Clenshaw–Curtis formula, the Basu formula and the Fejer formula of the first kind. |
| Databáze: | OpenAIRE |
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