AI 中文总结
针对有界域的自适应RBF多尺度逼近，通过采用拉格朗日表示法、排除压缩步骤将删除的函数值并结合局部拉格朗日函数，优化了核多尺度方法的自适应性能。
AI 中文摘要
本文研究核多尺度方法中的自适应问题。LeGia与Wendland于2014年已提出并分析了自适应压缩核多尺度逼近。本工作的主要贡献是尝试避免使用压缩步骤中最终会被删除的函数值；为处理函数值，我们始终采用拉格朗日表示法，仍假设可获取所有函数值以计算误差范数，但不将这些值纳入逼近过程，同时采用局部拉格朗日函数进一步减少数值计算量。
英文摘要
This article addresses adaptivity in the kernel multiscale method. Adaptively compressed kernel multiscale approximations have already been presented and analyzed in (LeGia & Wendland, 2014). The main contribution of this work is to attempt to avoid using function evaluations which will be deleted in the compression step anyways. In order to work with function values, we always work in the Lagrange representation. We still assume to have all function values available to compute error norms, but we do not include those values in our approximations. Finally, we also employ local Lagrange function to further reduce the numerical work.
