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 num...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.展开更多
Enlightened by Mal’cev theorem in universal algebra, a new criterion for consistency argument in λ-calculus has been introduced. It is equivalent to Jacopini and Baeten-Boerboom’ s, but more convenient to use. Base...Enlightened by Mal’cev theorem in universal algebra, a new criterion for consistency argument in λ-calculus has been introduced. It is equivalent to Jacopini and Baeten-Boerboom’ s, but more convenient to use. Based on the new criterion, one uses an enhanced technique to show a few results which provides a deeper insight in the classification problem of λ-terms with no normal forms.展开更多
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).
文摘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.
基金Project supported by the National 973 project of China: Mechanization of mathematics and Automata platform.
文摘Enlightened by Mal’cev theorem in universal algebra, a new criterion for consistency argument in λ-calculus has been introduced. It is equivalent to Jacopini and Baeten-Boerboom’ s, but more convenient to use. Based on the new criterion, one uses an enhanced technique to show a few results which provides a deeper insight in the classification problem of λ-terms with no normal forms.
