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
Copositive polynomial approximation
โ Scribed by Eli Passow; Louis Raymon
- Publisher
- Elsevier Science
- Year
- 1974
- Tongue
- English
- Weight
- 356 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
For a function f # L p [&1, 1], 0< p< , with finitely many sign changes, we construct a sequence of polynomials P n # 6 n which are copositive with f and such that & f &P n & p C| . ( f , (n+1) &1 ) p , where | . ( f , t) p denotes the Ditzian Totik modulus of continuity in L p metric. It was shown
It is known that shape preserving approximation has lower rates than unconstrained approximation. This is especially true for copositive and intertwining approximations. For f # L p , 1 p< , the former only has rate | . ( f, n &1 ) p , and the latter cannot even be bounded by C & f & p . In this pap