Bivariate hierarchical Hermite spline quasi-interpolation

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• 作者：Cesare Bracco ; Carlotta Giannelli ; Francesca Mazzia…
• 关键词：B ; splines ; Hermite quasi ; interpolation ; Hierarchical spaces ; Truncated hierarchical B ; splines
• 刊名：BIT Numerical Mathematics
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：56
• 期：4
• 页码：1165-1188
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Computational Mathematics and Numerical Analysis; Numeric Computing; Mathematics, general;
• 出版者：Springer Netherlands
• ISSN：1572-9125
• 卷排序：56

文摘

Spline quasi-interpolation (QI) is a general and powerful approach for the construction of low cost and accurate approximations of a given function. In order to provide an efficient adaptive approximation scheme in the bivariate setting, we consider quasi-interpolation in hierarchical spline spaces. In particular, we study and experiment the features of the hierarchical extension of the tensor-product formulation of the Hermite BS quasi-interpolation scheme. The convergence properties of this hierarchical operator, suitably defined in terms of truncated hierarchical B-spline bases, are analyzed. A selection of numerical examples is presented to compare the performances of the hierarchical and tensor-product versions of the scheme.