文章基本信息

标题：Quasi-Interpolation in Spline Spaces and Local Approximation Estimates
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作者：Maria E. Castillo ; Rita G. Figueroa ; Eduardo M. Garau 等
期刊名称：Mecánica Computacional
印刷版ISSN：2591-3522
出版年度：2019
卷号：37
期号：24
页码：967-967
出版社：CIMEC-INTEC-CONICET-UNL
摘要：The quasi-interpolation operators represent a practical and efficient method when calculating approximations using spline functions since they present a great simplicity and flexibility in their construction. To define them, B-splines bases are used and the coefficients are chosen locally, that is, each coefficient depends in general only on the data found in the support of the corresponding B-spline. The local form in which the coefficients for these operators are defined means that changes in the data or space of splines used have a low computational cost to recalculate the approximation, since it will change only locally. In this work we analyze Sobolev estimates for the approximation error using quasi-interpolants in spline spaces. We will establish in a general way the hypothesis about a quasi-interpolant to achieve the optimal orders of approximation. Finally, we propose simple but general quasi-interpolating constructions that satisfy the established hypotheses and we will compare experimentally the performance in the approximation for some of the proposed constructions.
关键词：spline approximation; stability; B-splines;