Optimally Localized Approximate Identities on the 2-Sphere
Optimally Localized Approximate Identities on the 2-Sphere
复制标题
2-球体上的最优局部近似恒等式
DOI：
10.1080/01630563.2011.587073
复制
发表时间：
2011
影响因子：
1.2
通讯作者：
V. Michel
中科院分区：
文献类型：
--
作者：
V. Michel
介绍了一种在2球上构造具有最优定位的近似恒等式的方法。这种方法可以在误差增加很小的情况下加速2球近似的计算。优化问题中的定位度量包含一个权函数，该权函数可以在一定的约束条件下选择。对于每一个权函数的选择，证明了最优核的存在唯一性以及在带宽有限情况下的近似恒等式的生成。此外，还计算了某权函数的最优局部化近似恒等式，并进行了数值验证。
We introduce a method to construct approximate identities on the 2-sphere that have an optimal localization. This approach can be used to accelerate the calculations of approximations on the 2-sphere essentially with a comparably small increase of the error. The localization measure in the optimization problem includes a weight function that can be chosen under some constraints. For each choice of weight function, existence and uniqueness of the optimal kernel are proved as well as the generation of an approximate identity in the bandlimited case. Moreover, the optimally localizing approximate identity for a certain weight function is calculated and numerically tested.