摘要
Nonlinear m-term approximation plays an important role in machine learning, signal processing and statistical estimating. In this paper by means of a nondecreasing dominated function, a greedy adaptive compression numerical algorithm in the best m -term approximation with regard to tensor product wavelet-type basis is pro-posed. The algorithm provides the asymptotically optimal approximation for the class of periodic functions with mixed Besov smoothness in the L q norm. Moreover, it depends only on the expansion of function f by tensor pro-duct wavelet-type basis, but neither on q nor on any special features of f.
Nonlinear m-term approximation plays an important role in machine learning, signal processing and statistical estimating. In this paper by means of a nondecreasing dominated function, a greedy adaptive compression numerical algorithm in the best m-term approximation with regard to tensor product wavelet-type basis is proposed. The algorithm provides the asymptotically optimal approximation for the class of periodic functions with mixed Besov smoothness in the Lq norm. Moreover, it depends only on the expansion of functionf by tensor product wavelet-type basis, but neither on q nor on any special features of f
基金
Supported by National Natural Science Foundation of China (No. 60872161, 10501026, 60675010 and 10626029)
Natural Science Foundation of Tianjin (No. 08JCYBJC09600)
China Postdoctoral Science Foundation ( No. 20070420708).
