MULTIVARIATE POLYNOMIAL APPROXIMATION IN THE HYPERCUBE

作者:Trefethen Lloyd N*
来源:PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145(11): 4837-4844.
DOI:10.1090/proc/13623

摘要

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 Euclidean degree, defined in terms of the 2-norm rather than the 1-norm of the exponent vector k of a monomial x (k1)(1) ... x (ks)(s) .

  • 出版日期2017-11