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若干周期再生核空间的覆盖数 被引量：1

The Covering Numbers for Some Periodic Reproducing Kernel Spaces
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摘要 借助离散Fourier变换给出估计Mercer核矩阵逆矩阵范数上界的一种方法,由此给出了估计周期再生核Hilbert空间覆盖数的上、下界的一般方法.特别,对两种特殊的周期再生核空间覆盖数的上、下界进行了比较. A kind of method of estimating the norm of the inverse of the periodic Mercer kernel matrices is proposed with discrete Fourier transforms,with which a general way of estimating the upper and lower bounds of the covering number for periodic reproducing kernel Hilbert spaces is provided. In particular,the lower and upper bounds of the covering number for two special periodic reproduced kernel spaces are compared.
作者 盛宝怀
机构地区 绍兴文理学院数学系
出处 《数学物理学报（A辑）》 CSCD 北大核心 2009年第6期1590-1600,共11页 Acta Mathematica Scientia
基金 国家自然科学基金(10871226)资助
关键词 再生核HILBERT空间 覆盖数 Fourier系数. Reproducing kernel Hilbert spaces Covering numbers Fourier coefficients.
分类号 O174.41 [理学—基础数学]
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共引文献11

同被引文献30

  • 1Wendland H. Scattered Data Approximation. Cambridge: Cambridge University Press, 2005.
  • 2Buhmann M D. Radial Basis Functions: Theory and Implementations. Cambridge: Cambridge University Press, 2003.
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  • 9Schaback R. Lower bounds for norms of inverses interpolation matrices for radial basis functions. J Approx Theory, 1994, 79(2): 287-306.
  • 10Zhou D X. The covering number in learning theory. J Complexity, 2002, 18(3): 739-767.

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数学物理学报（A辑）
2009年 第6期

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