Szegö quadrature formulas for certain Jacobi-type weight functions
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- by Leyla Daruis, Pablo González-Vera and Olav Njåstad PDF
- Math. Comp. 71 (2002), 683-701 Request permission
Abstract:
In this paper we are concerned with the estimation of integrals on the unit circle of the form $\int _0^{2\pi }f(e^{i\theta })\omega (\theta )d\theta$ by means of the so-called Szegö quadrature formulas, i.e., formulas of the type $\sum _{j=1}^n\lambda _jf(x_j)$ with distinct nodes on the unit circle, exactly integrating Laurent polynomials in subspaces of dimension as high as possible. When considering certain weight functions $\omega (\theta )$ related to the Jacobi functions for the interval $[-1,1],$ nodes $\{x_j\}_{j=1}^n$ and weights $\{\lambda _j\}_{j=1}^n$ in Szegö quadrature formulas are explicitly deduced. Illustrative numerical examples are also given.References
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Additional Information
- Leyla Daruis
- Affiliation: Department of Mathematical Analysis, La Laguna University, Tenerife, Canary Islands, Spain
- Email: ldaruis@ull.es
- Pablo González-Vera
- Affiliation: Corresponding author: Department of Mathematical Analysis, La Laguna University, 38271- La Laguna, Tenerife, Spain
- Email: pglez@ull.es. Fax: 34-922-318195
- Olav Njåstad
- Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway
- Email: njastad@math.ntnu.no
- Received by editor(s): February 11, 2000
- Received by editor(s) in revised form: July 10, 2000
- Published electronically: October 4, 2001
- Additional Notes: The work of the first author was performed as part of a grant of the Gobierno de Canarias.
The work of the second author was supported by the Scientific Research Project of the Spanish D.G.E.S. under contract PB96-1029. - © Copyright 2001 American Mathematical Society
- Journal: Math. Comp. 71 (2002), 683-701
- MSC (2000): Primary 41A55, 33C45
- DOI: https://doi.org/10.1090/S0025-5718-01-01337-0
- MathSciNet review: 1885621