The essential rate of approximation for radial function manifold  

作　　者：LIN ShaoBo CAO FeiLong XU ZongBeni 

机构地区：[1]Institute for Information and System Sciences, Xi'an Jiaotong University, Xi'an 710049, China [2]Institute of Metrology and Computational Sciences, China Jiliang University, Hangzhou 310018, China

出　　处：《Science China Mathematics》2011年第9期1985-1994,共10页中国科学：数学（英文版）

基　　金：supported by the National 973 Project (Grant No. 2007CB311002);National Natural Science Foundation of China (Grant Nos. 90818020,60873206)

摘　　要：In this paper, we investigate the radial function manifolds generated by a linear combination of radial functions. Let Wp^r（B^d） be the usual Sobolev class of functions on the unit ball 54. We study the deviation from the radial function manifolds to WP^r（b^d）. Our results show that the upper and lower bounds of approximation by a linear combination of radial functions are asymptotically identical. We also find that the radial function manifolds and ridge function manifolds generated by a linear combination of ridge functions possess the same rate of approximation.In this paper,we investigate the radial function manifolds generated by a linear combination of radial functions.Let Wpr(Bd) be the usual Sobolev class of functions on the unit ball B d.We study the deviation from the radial function manifolds to Wpr(Bd).Our results show that the upper and lower bounds of approximation by a linear combination of radial functions are asymptotically identical.We also find that the radial function manifolds and ridge function manifolds generated by a linear combination of ridge functions possess the same rate of approximation.

关 键 词：radial function rate of approximation Sobolev class ridge function 

分 类 号：O174.41[理学—数学] TP391.41[理学—基础数学]