Gauss quadratures and Jacobi matrices for weight functions not of one sign

Construction of Gauss quadratures with prescribed knots via Jacobi matrices is extended to the case where not all orthogonal polynomials exist due to the weight function changing sign. An algorithm is described and is demonstrated by calculating the knots of Kronrod schemes and other Gauss quadratur...

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Veröffentlicht in:	Mathematics of computation 1984, Vol.43 (168), p.543-550
Hauptverfasser:	KAUTSKY, J, ELHAY, S
Format:	Artikel
Sprache:	eng
Schlagworte:	Exact sciences and technology Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical approximation Sciences and techniques of general use
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	Construction of Gauss quadratures with prescribed knots via Jacobi matrices is extended to the case where not all orthogonal polynomials exist due to the weight function changing sign. An algorithm is described and is demonstrated by calculating the knots of Kronrod schemes and other Gauss quadratures with prescribed knots.
ISSN:	0025-5718 1088-6842
DOI:	10.1090/S0025-5718-1984-0758201-8