Compressed sensing approaches for polynomial approximation of high-dimensional functions

Understand

In recent years, the use of sparse recovery techniques in the approximation of high-dimensional functions has garnered increasing interest.

• In this work we present a survey of recent progress in this emerging topic.
• Our main focus is on the computation of polynomial approximations of high-dimensional functions on $d$-dimensional hypercubes.
• We show that smooth, multivariate functions possess expansions in orthogonal polynomial bases that are not only approximately sparse, but possess a particular type of structured sparsity defined by so-called lower sets.