A well-known result of Rivlin states that if \(p(z)\) is a polynomial of degree \(n\), such that \(p(z) \neq 0\) in \(|z|<1\), then \(\max _{1:} \quad, \quad|p(z)| \geqslant((r+1) / 2)^{n} \max _{1: 1},|p(z)|\). In this paper, we prove a generalization and refinements of this result. 1994 Academic P
On the maximum modulus of polynomials
β Scribed by N.K. Govil
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 212 KB
- Volume
- 112
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
p n, j (x)= \ n j + x j (1&x) n& j of a given function f (x) on [0, 1], besides the convergence and approximation, preserve some properties of the original function. For example: (i) if f (x) is non-decreasing, then for all n 1, the B n ( f; x) are nondecreasing; (ii) if f (x) is convex, then for
For a real polynomial f (X) of K variables the problem of finding max XβR K f (X) is investigated by reducing it to that of searching for the real roots of the univariate polynomial F (z) := j (zf (Ξ j )), where the product is extended over all the critical points Ξ j of f (X). Employment of the Her