Multivariate polynomial approximation in the hypercube
By Lloyd N. Trefethen. 2016
100 citations recorded by the source corpus.
A theorem is proved concerning approximation of analytic functions by multivariate polynomials in the $s$-dimensional hypercube. The geometric convergence rate is determined not by the usual notion of degree of a multivariate polynomial, but by the {\it Euclidean degree,} defined in terms of the 2-norm rather than the 1-norm of the exponent vector $\bf k$ of a monomial $x_1^{k_1}\cdots \kern .8pt x_s^{k_s}$.
Subfields: Applied Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/52b6b3b9a64c7eaac3da8d2246a0332b16d51c1b
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In Applied Mathematics
In Numerical Analysis
Citations in the corpus
- Neural-Fly enables rapid learning for agile flight in strong winds (2022, background): “We first introduce the following multivariate polynomial approximation lemma in the hypercube proved in [55].”
- Meta-Adaptive Nonlinear Control: Theory and Algorithms (2021, background): “The intuition behind this structure is that, any analytic function f̄(x, c̄) can be approximated by φ(x)c(c̄) with a universal approximator φ [34].”