Integral error formulae for the scale of mean value interpolations which includes Kergin and Hakopian interpolation
by Shayne Waldron
In this paper, we provide an integral error formula for a certain
scale of mean value interpolations
which includes the multivariate polynomial interpolation
schemes of Kergin and Hakopian.
This formula involves only derivatives of order one higher than
the degree of the interpolating polynomial space, and from it we can obtain
sharp $L_\infty$-estimates. These $L_\infty$-estimates are precisely those that
numerical analysts want, to guarantee that a scheme based on such an
interpolation has the maximum possible order.
scale of mean value interpolations, Kergin interpolation,
Hakopian interpolation, Lagrange interpolation, Hermite interpolation,
Hermite-Genocchi formula, multivariate divided difference, plane wave, lifting,
Math Review Classification:
41A05, 41A63, 41A80 (primary), 41A10, 41A44, 44A12 (secondary)
Written in TeX. This paper is the basis of Chapter 1 of Shayne Waldron's
24 October 1997
Appeared in Numer. Math. 77 (1997), no. 1, 105--122.
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