## Anti-Szego quadrature rules

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- by Sun-Mi Kim and Lothar Reichel;
- Math. Comp.
**76**(2007), 795-810 - DOI: https://doi.org/10.1090/S0025-5718-06-01904-1
- Published electronically: November 28, 2006
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## Abstract:

Szegő quadrature rules are discretization methods for approximating integrals of the form $\int _{-\pi }^{\pi } f(e^{it}) d\mu (t)$. This paper presents a new class of discretization methods, which we refer to as anti-Szegő quadrature rules. Anti-Szegő rules can be used to estimate the error in Szegő quadrature rules: under suitable conditions, pairs of associated Szegő and anti-Szegő quadrature rules provide upper and lower bounds for the value of the given integral. The construction of anti-Szegő quadrature rules is almost identical to that of Szegő quadrature rules in that pairs of associated Szegő and anti-Szegő rules differ only in the choice of a parameter of unit modulus. Several examples of Szegő and anti-Szegő quadrature rule pairs are presented.## References

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## Bibliographic Information

**Sun-Mi Kim**- Affiliation: Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
- Email: sukim@math.kent.edu
**Lothar Reichel**- Affiliation: Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
- Email: reichel@math.kent.edu
- Received by editor(s): October 12, 2004
- Received by editor(s) in revised form: September 23, 2005
- Published electronically: November 28, 2006
- Additional Notes: Research supported in part by NSF grant DMS-0107858.
- © Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp.
**76**(2007), 795-810 - MSC (2000): Primary 65D32, 42A10; Secondary 30E20
- DOI: https://doi.org/10.1090/S0025-5718-06-01904-1
- MathSciNet review: 2291837