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We address classic multivariate polynomial regression tasks from a novelperspective resting on the notion of general polynomial $l_p$-degree, withtotal, Euclidean, and maximum degree being the centre of considerations. Whileensuring stability is a theoretically known and empirically observablelimitation 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. Wecomplement the novel regression scheme, presented herein, by an adaptive domaindecomposition approach that extends the stability for fast functionapproximation even further.

Multivariate Polynomial Regression of Euclidean Degree Extends the Stability for Fast Approximations of Trefethen Functions