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Strong unicity of best uniform approximation from periodic spline spaces

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons45792

Zeilfelder,  Frank
Computer Graphics, MPI for Informatics, Max Planck Society;

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Zeilfelder, F. (1999). Strong unicity of best uniform approximation from periodic spline spaces. Journal of Approximation Theory, 99(2), 1-29.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-36E4-4
Abstract
In this paper we give a complete characterization of the strongly unique best uniform approximation from periodic spline spaces. We distinguish between even-dimensional and odd-dimensional periodic spline spaces. These spaces are weak Chebyshev if and only if their dimension is odd. We show that the stongly unique best approximation from periodic spline spaces of odd dimension can be characterized alone by alternation properties of the error. This is not the case for even dimension. In this case an additional interpolation condition arises in our characterization.