On “best” interpolation
1976; Elsevier BV; Volume: 16; Issue: 1 Linguagem: Inglês
10.1016/0021-9045(76)90093-9
ISSN1096-0430
Autores Tópico(s)Mathematical Approximation and Integration
ResumoRecent interest in the problem of minimizing ∥f(k)∥∞ under the constraint that fti) = f0(ti), i = 1,…, n + k, for some given f0 and given (ti)1n+k seems to make it worthwhile to explain how Favard solved this problem in the thirties, particularly since Favard's paper on the subject is rather sketchy in places. The explanation is given in terms of a dual problem, using a technique initiated by M. Krein. In addition, the analogous problem of minimizing ∥f(k)∥p for 1 ⩽ p < ∞ under similar constraints is discussed.
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