Title: Quadrature formulas based on rational interpolation
Authors: Van Assche, Walter ×
Vanherwegen, I #
Issue Date: 1993
Publisher: Amer mathematical soc
Series Title: Mathematics of computation vol:61 issue:204 pages:765-783
Abstract: We consider quadrature formulas based on interpolation using the basis functions 1/(1 + t(k)x) (k = 1 , 2, 3, ... ) on [-1, 1], where t(k) are parameters on the interval (-1, 1) . We investigate two types of quadratures: quadrature formulas of maximum accuracy which correctly integrate as many basis functions as possible (Gaussian quadrature), and quadrature formulas whose nodes are the zeros of the orthogonal functions obtained by orthogonalizing the system of basis functions (orthogonal quadrature). We show that both approaches involve orthogonal polynomials with modified weights which depend on the number of quadrature nodes. The asymptotic distribution of the nodes is obtained as well as various interlacing properties and monotonicity results for the nodes.
ISSN: 0025-5718
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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