Nonlinear function approximation: Computing smooth solutions with an adaptive greedy algorithm

Opposed to linear schemes, nonlinear function approximation allows to obtain a dimension independent rate of convergence. Unfortunately, in the presence of data noise typical algorithms (like e. g., backpropagation) are inherently unstable, whereas greedy algorithms, which are in principle stable, can not be implemented in their original form, since they require unavailable information about the data. In this work we present a modified greedy algorithm, which does not need this information, but rather recovers it iteratively from the given data. We show that the generated approximations are always at least as smooth as the original function and that the algorithm also remains stable, when it is applied to noisy data. Finally the applicability of this algorithm is demonstrated by numerical experiments.

• Type: Journal
• Year: 2006
• Where: JAT
• Authors: Andreas Hofinger
• Keywords: Algorithm, Greedy Algorithm, JAT 2006, Nonlinear Function Approximation