Quadrature formulas based on rational interpolation
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- by Walter Van Assche and Ingrid Vanherwegen PDF
- Math. Comp. 61 (1993), 765-783 Request permission
Abstract:
We consider quadrature formulas based on interpolation using the basis functions $1/(1 + {t_k}x)\quad (k = 1,2,3, \ldots )$ 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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Math. Comp. 61 (1993), 765-783
- MSC: Primary 65D32; Secondary 41A05, 41A55, 42C05
- DOI: https://doi.org/10.1090/S0025-5718-1993-1195424-6
- MathSciNet review: 1195424