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.

翻译：我们从新颖的角度处理传统的多变量多元回归任务,其依据是普通多数值 $l_p$-corm的概念,整体而言,Euclidean 和最大程度是考虑的中心。虽然确保稳定是理论上已知的、经验上可以观察到的对任何计算计划的一种限制,以快速功能近似为目的,但我们表明选择欧clidean 度最能抵御不稳定现象。特别是,对于一类分析功能,我们称之为Trefethen 函数,我们扩展了最近的论点,认为这一结果是真实的。我们通过一个适应性域分解法来补充我们在这里提出的新的回归计划,该套法将快速功能的稳定性进一步扩大至更远。