B-spline quasi-interpolation on sparse grids

Authors:
Ying Jiang;Yuesheng Xu
Affiliations:
Department of Scientific Computing and Computer Applications, Sun Yat-sen University, Guangzhou 510275, PR China;Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA and Department of Scientific Computing and Computer Applications, Sun Yat-sen University, Guangzhou 510275, PR China
Venue:
Journal of Complexity
Year:
2011

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Abstract

We propose a periodic B-spline quasi-interpolation for multivariate functions on sparse grids and develop a fast scheme for the evaluation of a linear combination of B-splines on sparse grids. We prove that both of these operations require only O(nlog^d^-^1n) number of multiplications, where n is the number of univariate B-spline basis functions used in each coordinate direction and d is the number of variables of the functions. We also establish the optimal approximation order of the periodic B-spline quasi-interpolation. Numerical examples are presented to confirm the theoretical estimates.