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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

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✦ 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.