论文标题
欧几里得度的多元多项式回归扩展了Trefethen函数快速近似的稳定性
Multivariate Polynomial Regression of Euclidean Degree Extends the Stability for Fast Approximations of Trefethen Functions
论文作者
论文摘要
我们从一个新的角度解决了经典的多种多项式回归任务，该任务基于一般多项式$ l_p $ -Degree的概念，总计，欧几里得和最大程度是考虑因素的中心。在确保稳定性是对寻求快速功能近似的任何计算方案的理论上已知且可观察到的限制，但我们表明，选择欧几里得学位可抵抗不稳定现象。特别是，对于一类分析功能，我们称为Trefethen功能，我们扩展了最新的论点，这些论点表明这是真实的。我们通过一种自适应结构域分解方法来补充本文介绍的新型回归方案，该方法扩展了快速函数近似的稳定性。
We address classic multivariate polynomial regression tasks from a novel perspective resting on the notion of general polynomial $l_p$-degree, with total, Euclidean, and maximum degree being the centre of considerations. While ensuring stability is a theoretically known and empirically observable limitation of any computational scheme seeking for fast function approximation, we show that choosing Euclidean degree resists the instability phenomenon best. Especially, for a class of analytic functions, we termed Trefethen functions, we extend recent argumentations that suggest this result to be genuine. We complement the novel regression scheme, presented herein, by an adaptive domain decomposition approach that extends the stability for fast function approximation even further.
