Some extremal properties of multivariate polynomial splines in the metric Lp (Rd ) |
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Institution: | Department of Mathematics, Beijing Normal University, Beijing 100875, China |
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Abstract: | We constructed a kind of continuous multivariate spline operators as the approximation tools of the multivariate functions on the Bd instead of the usual multivariate cardinal interpolation oper-ators of splines, and obtained the approximation error by this kind of spline operators. Meantime, by the results, we also obtained that the spaces of multivariate polynomial splines are weakly asymptoti-cally optimal for the Kolmogorov widths and the linear widths of some anisotropic Sobolev classes of smooth functions on Bd in the metric Lp(Bd). |
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Keywords: | multivariate polynomial splines infinite-dimensional width optimal subspace Sobolev classes |
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