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中文摘要：
矩形网格上带缺项的二元插值方法在数值分析、计算机辅助几何设计、数字图像修复等领域有着广泛的应用。本文在矩形网格上构造二元重心有理插值。首先基于Lebesgue常数最小建立优化模型,求解获得最优权,其次以插值曲面的能量最小获得缺项插值条件,最后数值实例表明新方法的可行性。
英文摘要：
Bivariate barycentric rational interpolation over lacunary rectangular grids has a wide range of applications in numerical analysis,CAGD and digital image inpainting.In this paper,a new bivariate barycentric rational interpolation is presented based on the Minimizing Lebesgue Constant over lacunary rectangular grids.Firstly,optimal weights are obtained by solving the optimal model which is established based on the minimal Lebesgue constant.Then,the lacunary interpolation conditions are given based on the minimal energy function.Finally,numerical example is given to demonstrate the feasibility of the new approach.
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Lebesgue Constant Minimizing Shape Preserving Barycentric Rational Interpolation Optimization algori
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