Integral error formulæ for the scale of mean value interpolations which includes Kergin and Hakopian interpolation
نویسنده
چکیده
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∞-estimates. These L∞-estimates are precisely those that numerical analysts want, to guarantee that a scheme based on such an interpolation has the maximum possible order.
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UNIVERSITY OF WISCONSIN-MADISON CENTER FOR THE MATHEMATICAL SCIENCES Integral error formul for the scale of mean value interpolations which includes Kergin and Hakopian interpolation
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 L1-estimates. These L1-estimates are precisely those that num...
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