Given gridded cell-average data of a smooth multivariate function, we present a constructive explicit procedure for generating a high-order global approximation of the function. One contribution is the derivation of high order approximations to point-values of the function directly from the cell-average data. The second contribution is the development of univariate B-spline based high order quasi-interpolation operators using cell-average data. Multivariate spline quasi-interpolation approximation operators are obtained by tensor products of the univariate operators.

翻译：根据光滑多变量函数的网格平均单元格数据,我们提出了一个建设性的明确程序,用于生成该函数的高顺序全球近似值。一个贡献是,从单元格平均数据中直接得出该函数的点值的高排序近近似值。第二个贡献是,利用单元格平均数据开发基于单ivariate B-spline的高序准内插操作员。多变量螺旋准内插操作员由单项操作员的高压产品获得。