✦ LIBER ✦
Lagrange and Least-Squares Polynomials as Limits of Linear Combinations of Iterates of Bernstein and Durrmeyer Polynomials
✍ Scribed by J.C. Sevy
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 139 KB
- Volume
- 80
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
✦ Synopsis
The linear combination of iterates (1-\left(1-P_{n}\right)^{M}) of Bernstein and Durrmeyer operators of a fixed degree (n) is considered for increasing order of iteration (M). The resulting sequence of polynomials is shown to converge to the Lagrange interpolating polynomial for the Bernstein operators, and the least-squares approximating polynomial for the Durrmeyer operators. 1995 Academic Press, Inc.