Theory and numerical implementation of greedy algorithms in highly nonlinear approximation

Greedy algorithms in nonlinear approximation have been studied in mathematics, signal processing, and statistics. In this thesis, they are investigated as part of approximation theory, with applications to one-dimensional signal processing.; Necessary background is given for understanding the germane properties of bases. Atoms and redundant dictionaries are introduced. Approximation results of greedy algorithms are stated. The computational complexity of greedy algorithms is discussed.; Some ways that greedy algorithms can be rendered tractable are considered. Past numerical implementation of greedy algorithms are examined, as are possible adaptations. Theoretical aspects and practical issues of implementation are discussed.