积分算子核的正则化与张量小波积压缩
Regularization and compression of integral operator kernels with tensor paraproducts
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中文总结 AI 辅助
本文提出一种新视角，通过拟线性化距离的张量Haar展开上的非线性变换，得到主项和残差项的新表示，增强局部正则性并实现O(N)存储，数值实验验证了势核的有效性。
中文摘要 AI 辅助
我们提出了对由距离的非线性函数给出的积分算子核的新视角。该视角之所以有用，是因为它允许对作用于距离d(x,y)的张量Haar展开上的非线性变换进行拟线性化。这导致了一种由主项和残差项组成的新表示，具有理想的特性；即，主分量的局部正则性增强（在某些情况下，快速的非对角衰减导致O(N)存储），以及由于全局正则性增强而改进逼近的残差展开。文中包含了势核的数值实验。
英文摘要
We present a new perspective on integral operator kernels given by a nonlinear function of the distance. This perspective is useful since it permits one to quasilinearize the nonlinear transformations acting on the tensor Haar expansion of the distance, d(x,y). This leads to a new representation comprised of a principal and residual term with desirable features; namely, enhanced local regularity of the principal component (and in certain situations rapid off-diagonal decay leading to O(N) storage) and a residual expansion of improved approximation as a consequence of enhanced global regularity. Numerical experiments on the potential kernel are included
发表机构
- Yale University（耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。
