This article is cited in 3 papers

On approximation of multivalued mapping by algebraic polynomial with constraints

I. Yu. Vygodchikova

Chair of Mathematical Economy, Saratov State University, 83 Astrahanskaya str., Saratov, 410012 Russia

Abstract: We consider a discrete problem of the best uniform approximation of multivalued mapping by segment images by an algebraic polynomial with constraints upon the value of the approximating polynomial in several nodes of a grid. We establish a criterion of optimality of the solution, which is a generalization of the P. L. Chebyshev's alternance.

Keywords: multivalued mapping, approximating polynomial, alternance optimality conditions.

UDC: 517.518+519.651

Received: 01.08.2013

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:2, 25–28

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