We discuss the degree of approximation by polynomials of a function f that is piecewise monotone in [&1, 1]. We would like to approximate f by polynomials which are comonotone with it. We show that by relaxing the requirement for comonotonicity in small neighborhoods of the points where changes in m
Comonotone polynomial approximation
โ Scribed by Eli Passow; Louis Raymon; John A Roulier
- Publisher
- Elsevier Science
- Year
- 1974
- Tongue
- English
- Weight
- 168 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let f be a continuous function on [&1, 1], which changes its monotonicity finitely many times in the interval, say s times. We discuss the validity of Jackson-type estimates for the approximation of f by algebraic polynomials that are comonotone with it. While we prove the validity of the Jackson-ty
We prove that if a function \(f \in \mathbb{C}[0,1]\) changes sign finitely many times, then for any \(n\) large enough the degree of copositive approximation to \(f\) by quadratic spliners with \(n-1\) equally spaced knots can be estimated by \(C \omega_{2}(f, 1 / n)\), where \(C\) is an absolute c