Simultaneous best approximation by three polynomials

Kannan, V. ; Ravichandran, S. (1989) Simultaneous best approximation by three polynomials Journal of Approximation Theory, 59 (3). pp. 258-266. ISSN 0021-9045

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/002190...

Related URL: http://dx.doi.org/10.1016/0021-9045(89)90089-0

Abstract

Let [a, b] be any interval and let p0, p1, pk be any three polynomials of degrees 0, 1, k, respectively, where k ≥ 2. A set of necessary and sufficient conditions for the existence of an f in C[a, b] such that pi is the best approximation to f from the space of all polynomials of degree less than or equal to i, for all i = 0, 1, k, is given.

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