Rescaled Pure Greedy Algorithm for Hilbert and Banach Spaces
arXiv:1505.0360413 citations
Originality Incremental advance
AI Analysis
For researchers in approximation theory and signal processing, this provides a simple algorithm with provably optimal rates, though it is an incremental improvement over existing greedy methods.
The paper introduces a modification of the Pure Greedy Algorithm that achieves optimal convergence rates for sparse approximation in Hilbert and Banach spaces, specifically on the class of convex combinations of dictionary elements.
We show that a very simple modification of the Pure Greedy Algorithm for approximating functions by sparse sums from a dictionary in a Hilbert or more generally a Banach space has optimal convergence rates on the class of convex combinations of dictionary elements