Convergence of modified approximants associated with orthogonal rational functions
✍ Scribed by A. Bultheel; P. González-Vera; E. Hendriksen; O. Njåstad
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 391 KB
- Volume
- 57
- Category
- Article
- ISSN
- 0377-0427
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📜 SIMILAR VOLUMES
Rational functions orthogonal on the unit circle with prescribed poles are studied. We establish some convergence theorems for the orthogonal rational functions. We generalize some of the results for Szeg6 polynomials to rational orthogonal functions.
This paper investigates the convergence condition for the polynomial approximation of rational functions and rational curves. The main result, based on a hybrid expression of rational functions (or curves), is that two-point Hermite interpolation converges if all eigenvalue moduli of a certain r\_r
analytic in a neighborhood of infinity will be approximated by Pade approximants. In a first group of results rather strong assumptions are made about the singularities of the function f to be approximated (Assumption 1.1). In a second group (Definition 1.3 and Theorem 1.7) a different type of assum