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Title: Orthogonal Laurent polynomials and quadrature formulas for unbounded intervals: I. Gauss-type formulas
Authors: Bultheel, Adhemar ×
Diaz-Mendoza, Carlos
González-Vera, Pablo
Orive, Ramon #
Issue Date: 2003
Publisher: Rocky Mountain Mathematics Consortium
Series Title: The Rocky Mountain journal of mathematics vol:33 issue:2 pages:585-608
Conference: 2001: A Mathematical Odyssey location:Mesa State College, Grand Junction, CO date:6-10 August 2001
Abstract: We study the convergence of quadrature formulas for integrals over the positive real line with an arbitrary distribution function. The nodes of the quadrature formulas are the zeros of orthogonal Laurent polynomials with respect to the distribution function and with respect to a certain nesting. This ensures a maximal domain of validity and the quadratures are therefore called Gauss-type formulas. The class of functions for which convergence holds is characterized in terms of the moments of the distribution function. Moreover, error estimates are given when f satisfies certain continuity conditions. Finally, these results are applied to the family of distributions dφ(x) = x^α exp{-(x^(γ_1) + x^(-γ_2))) dx, γ_1,γ_2 greater than or equal to 1/2, α is an element of R.
Description: editors: Bonan-Hamada, Cathy and Gustafson, Phil
URI: 
ISSN: 0035-7596
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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