Naslov
On the existence of the best discrete approximation in l_p norm by reciprocals of real polynomials

Autori
Jukić, Dragan

Izvornik
Journal of Approximation Theory (0021-9045) 156 (2009), 2; 212-222

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
reciprocals of polynomials; data fitting; discrete rational approximation; existence problem

Sažetak
For the given data $(w_i, x_i, y_i)$, $i=1, \ldots, M$, we consider the problem of existence of the best discrete approximation in $l_p$ norm ($1\leq p<\infty$) by reciprocals of real polynomials. For this problem, the existence of best approximations is not always guaranteed. In this paper, we give a condition on data which is necessary and sufficient for the existence of the best approximation in $l_p$ norm. This condition is theoretical in nature. We apply it to obtain several other existence theorems very useful in practice. Some illustrative examples are also included.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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