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On Best Approximation of the Monomials on the Unit Ball of Rr

✍ Scribed by Ulrike Maier

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 335 KB
Volume: 92
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1996.3110

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✦ Synopsis

Bos and Liang have separately proved that the Kergin interpolants with respect to distinguished nodes on the unit disk are best approximations of the monomials in the infinity norm. These results are extended by characterizing the nodes as solutions of a system of nonlinear equations. Thus, it is possible to get all nodes with this property on the unit disk and it is likewise possible to lift results to the ball in the sense of approximation in the mean.

1998 Academic Press * r + is defined to be the linear space of homogeneous polynomials of degree +.

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