Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1203.65054
Bultheel, A.; González-Vera, P.; Hendriksen, E.; Njåstad, O.
Rational quadrature formulas on the unit circle with prescribed nodes and maximal domain of validity.
(English)
[J] IMA J. Numer. Anal. 30, No. 4, 940-963 (2010). ISSN 0272-4979; ISSN 1464-3642/e

The authors study quadrature formulas of the form $$\int_{-\pi}^{\pi} f(e^{i\theta})\, d\mu(\theta) \approx \sum_{k=1}^n \lambda_k\, f(z_k),$$ where $\mu$ is a positive Borel measure, $\lambda_k>0$ and $z_k$ are nodes on the complex unit circle. It is shown that the quadrature formulas can be chosen to be exact in certain subspaces of rational functions of dimension $2n$. Rational Szegö-Radau and Szegö-Lobatto quadrature formulas, where one or two nodes are prescribed, are characterized too. Thus this paper generalizes results of {\it C.~Jagels} and {\it L.~Reichel} [J. Comput. Appl. Math. 200, No.~1, 116--126 (2007; Zbl 1109.65027)] from trigonometric polynomials to rational functions.
[Manfred Tasche (Rostock)]
MSC 2000:

Citations: Zbl 1109.65027

Highlights
Master Server