Note on approximating complex zeros of a polynomial
โ Scribed by Bernard Friedman
- Publisher
- John Wiley and Sons
- Year
- 1949
- Tongue
- English
- Weight
- 513 KB
- Volume
- 2
- Category
- Article
- ISSN
- 0010-3640
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
By establishing an identity for \(S_{n}(x):=\sum_{j=0}^{n}|j / n-x|\left({ }_{j}^{n}\right) x^{j}(1-x)^{n-j}\), the present paper shows that a pointwise asymptotic estimate cannot hold for \(S_{n}(x)\), and, at the same time, obtains a better result than that in Bojanic and Cheng [3]. 1993 Academic
Let E be a subspace of C(X) and let R(E)= gรh: g, h # E ; h>0]. We make a simple, yet intriguing observation: if zero is a best approximation to f from E, then zero is a best approximation to f from R(E ). We also prove that if That extends the results of P. Borwein and S. Zhou who proved it for t
It is shown that if weighted polynomials w n P n with deg P n n converge uniformly on the support of the extremal measure associated with w, then they converge to 0 everywhere else. It is also shown that uniform approximation on the support can always be characterized by a closed subset Z having the