多元多元多项式回归的欧氏度扩展了Trefethen函数快速逼近的稳定性
Multivariate Polynomial Regression of Euclidean Degree Extends the Stability for Fast Approximations of Trefethen Functions
摘要：
我们解决经典的多元多项式回归任务，从一个新的角度休息的概念，一般的多项式$l_p$度，总，欧几里德，最大程度的中心考虑。虽然确保稳定性是一个理论上已知的和经验上可观察到的任何计算方案寻求快速函数逼近的限制，我们表明，选择欧几里德度抵抗不稳定现象最好。特别地，对于一类解析函数，我们称之为Trefethen函数，我们推广了最近的证明，表明这一结果是真实的。我们补充了新的回归方案，本文提出的自适应区域分解方法，扩展了快速函数逼近的稳定性，甚至进一步。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
