Nonlinear approximation in finite-dimensional spaces (Q1383443)

The authors study certain problems of nonlinear approximation which arise in image processing. They take a Banach space \(X\) and a subset \(D\) of \(X\) whose linear span is dense in \(X\), and they consider approximation in finite-dimensional Euclidean spaces equipped with various norms for studying the relationship between the size of \(D\) and its approximation power. Also, they show how to appropriately choose sets \(D\) for which the greedy algorithms achieve estimates similar to those of best \(m\)-term approximation.