Orthogonal projection and minimal linear interpolation on a n-dimensional cube
Abstract
Let H be the orthogonal projection onto polynomials of n variables of degree < 1 and \\ \\ be the norm of an operator from C ([0,1]n) to C ([0,1]n). In this paper we show that C1On <= \\H\\ <= C2On, n G N. Here On denotes the minimal norm of a projection dealing with the linear interpolation on the cube [0,1]n. The proofs make use of certain properties of the Eulerian numbers and the central B-splines and also some previous results of the author.
References
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Review
For citations:
Nevskij M.V. Orthogonal projection and minimal linear interpolation on a n-dimensional cube. Modeling and Analysis of Information Systems. 2007;14(3):8-28. (In Russ.)
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