Optimal approximation of infinite-dimensional holomorphic functions

Understand

Over the last decade, approximating functions in infinite dimensions from samples has gained increasing attention in computational science and engineering, especially in computational uncertainty quantification.

• This is primarily due to the relevance of functions that are solutions to parametric differential equations in various fields, e.g.
• chemistry, economics, engineering, and physics.
• While acquiring accurate and reliable approximations of such functions is inherently difficult, current benchmark methods exploit the fact that such functions often belong to certain classes of holomorphic functions to get algebraic convergence rates in infinite dimensions with respect to the number of (potentially adaptive) samples $m$.