Constructive sparse trigonometric approximation for functions with small mixed smoothness
arXiv:1503.00282v131 citations
AI Analysis
This work addresses a theoretical approximation problem for researchers in numerical analysis and harmonic analysis, but appears incremental as it builds on existing methods for mixed smoothness classes.
The paper tackles the problem of approximating functions with small mixed smoothness using m-term trigonometric approximations, and presents a constructive greedy algorithm that achieves the best possible order of approximation error.
The paper gives a constructive method, based on greedy algorithms, that provides for the classes of functions with small mixed smoothness the best possible in the sense of order approximation error for the $m$-term approximation with respect to the trigonometric system.