On Product Integration with Gauss-Kronrod Nodes

Gauss-Kronrod product quadrature formulas for the numerical approximation of ∫1 -1k(x)f(x) dx are shown to converge for every Riemann integrable f, and to possess optimal stability. Similar results are proved for the product formulas based on the Kronrod nodes only. An application to the uniform con...

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Veröffentlicht in:	SIAM journal on numerical analysis 1998-02, Vol.35 (1), p.78-92
1. Verfasser:	Ehrich, Sven
Format:	Artikel
Sprache:	eng
Schlagworte:	Alliances Approximation Differential equations Exact sciences and technology Gaussian quadratures Integral equations Mathematical functions Mathematical integration Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical approximation Numerical integration 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 Numerical quadratures Perceptron convergence procedure Polynomials Sciences and techniques of general use
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Beschreibung
Zusammenfassung:	Gauss-Kronrod product quadrature formulas for the numerical approximation of ∫1 -1k(x)f(x) dx are shown to converge for every Riemann integrable f, and to possess optimal stability. Similar results are proved for the product formulas based on the Kronrod nodes only. An application to the uniform convergence of approximate solutions of integral equations is given.
ISSN:	0036-1429 1095-7170
DOI:	10.1137/S0036142995295790