Polynomial Approximation of Anisotropic Analytic Functions of Several Variables

• Published in: Constructive approximation Vol. 53; no. 2; pp. 319 - 348
• Main Authors: Bonito, Andrea, DeVore, Ronald, Guignard, Diane, Jantsch, Peter, Petrova, Guergana
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2021; Springer Nature B.V
• Subjects: Analysis; Analytic functions; Approximation; Budgets; Mathematics; Mathematics and Statistics; Numerical Analysis; Numerical methods; Partial differential equations; Polynomials; 65N15; Anisotropic analyticity; 41A58; 41A63; Approximations and expansions; 41A10; Parametric PDEs

Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomials. We introduce various anisotropic model classes based on Taylor expansions, and study their approximation by finite d...