Multivariate approximation

点击翻译按钮获取中文摘要

Approximation theory studies the ability to approximate general, possibly complicated, functions by simpler and more easily calculated functions. Many problems in approximation theory of functions of one variable have been solved. However, the methods do not always easily generalize to the approximation of functions of several variables. The main goal of my proposed research is to develop existing and create new methods for the approximation of functions of several variables. I will focus on questions related to measures of smoothness (how can we easily measure or "predict" the accuracy of approximation) and shape preserving approximation (if the target function has a certain shape, how to construct an approximation which also possesses such a shape).