The work of P. Turán on interpolation and approximation
✍ Scribed by G.G Lorentz
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 310 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
For a family of r-graphs F; the Tur! a an number exðn; FÞ is the maximum number of edges in an n vertex r-graph that does not contain any member of F: The Tur! a an density When F is an r-graph, pðFÞ=0; and r > 2; determining pðFÞ is a notoriously hard problem, even for very simple r-graphs F: For
For \(f \in C[-1,1]\) denote by \(B\_{n, p}(f)\) its best \(L\_{n}\)-approximant by polynomials of degree at most \(n(1 \leqslant p \leqslant \infty)\). The following statement is the main result of the paper: Let \(1 1\). 1993 Academic Press, Inc.
The L m extremal polynomials in an explicit form with respect to the weights (1&x) &1Â2 (1+x) (m&1)Â2 and (1&x) (m&1)Â2 (1+x) &1Â2 for even m are given. Also, an explicit representation for the Cotes numbers of the corresponding Tura n quadrature formulas and their asymptotic behavior is provided. 1