## Abstract

Classical interpolatory or Gaussian quadrature formulas are exact on sets of polynomials. The Szegő quadrature formulas are the analogs for quadrature on the complex unit circle. Here the formulas are exact on sets of Laurent polynomials. In this paper we consider generalizations of these ideas, where the (Laurent) polynomials are replaced by rational functions that have prescribed poles. These quadrature formulas are closely related to certain multipoint rational approximants of Cauchy or Riesz–Herglotz transforms of a (positive or general complex) measure. We consider the construction and properties of these approximants and the corresponding quadrature formulas as well as the convergence and rate of convergence.

## Full Text

### Topics from this Paper

- Sets Of Polynomials
- Quadrature Formulas
- Orthogonal Rational Functions
- Complex Unit Circle
- Gaussian Quadrature Formulas + Show 5 more

Create a personalized feed of these topics

Get Started#### Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call### Similar Papers

- Journal of Computational and Applied Mathematics
- Aug 1, 2015

- Mathematische Nachrichten
- Jan 1, 2008

- Applied Numerical Analysis & Computational Mathematics
- Dec 1, 2004

- Advances in Engineering Software
- Aug 1, 2009

- IMA Journal of Numerical Analysis
- Oct 1, 2010

- Applied Numerical Mathematics
- Dec 1, 2010

- Mathematics of Computation
- Feb 24, 1999

- Journal of Computational and Applied Mathematics
- Apr 1, 2003

- Mathematics of Computation
- Oct 4, 2005

- Dec 3, 2017

- Journal of Computational and Applied Mathematics
- Dec 1, 1995

- IMA Journal of Numerical Analysis
- Oct 1, 2006

- Journal of Complexity
- Jun 1, 2003

- Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series
- Oct 7, 2021

### Journal of Computational and Applied Mathematics

- Journal of Computational and Applied Mathematics
- Dec 1, 2023

- Journal of Computational and Applied Mathematics
- Dec 1, 2023

- Journal of Computational and Applied Mathematics
- Dec 1, 2023

- Journal of Computational and Applied Mathematics
- Dec 1, 2023

- Journal of Computational and Applied Mathematics
- Dec 1, 2023

- Journal of Computational and Applied Mathematics
- Dec 1, 2023

- Journal of Computational and Applied Mathematics
- Dec 1, 2023

- Journal of Computational and Applied Mathematics
- Dec 1, 2023

- Journal of Computational and Applied Mathematics
- Dec 1, 2023

- Journal of Computational and Applied Mathematics
- Dec 1, 2023