On the rate of convergence of hermite-fejér polynomials to functions of bounded variation on the zeros of certain jacobi polynomials
In this paper, we study the Hermite-Fejér interpolation, Hn(f,x), for a function f of bounded variation on [-1,1] when the inter)olation is taken over the zeros of Jacobi polynomials, Pn (∝,β ) (x) when |∝|, | β| ≤ ½.Our main result is an estimate for the rate of convergence of Hn(f,x) at points of...
- Autores:
-
Al-Jarrah, Radwan
Rababah, Abedallah
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 1990
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/43271
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/43271
http://bdigital.unal.edu.co/33369/
- Palabra clave:
- Hermite-Fejér interpolation
function
Jacobi polynomials
rate convergence points of continuity
zeros of the Legendre polynomials
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | In this paper, we study the Hermite-Fejér interpolation, Hn(f,x), for a function f of bounded variation on [-1,1] when the inter)olation is taken over the zeros of Jacobi polynomials, Pn (∝,β ) (x) when |∝|, | β| ≤ ½.Our main result is an estimate for the rate of convergence of Hn(f,x) at points of continuity of f,and a special attention is given to the interpolation over the zeros of the Legendre polynomials. |
|---|