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周期函数的数值微分问题 被引量：5

Numerical Differentiation for Periodic Functions and Its Applications
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摘要 用Tikhonov正则化方法讨论了周期函数的数值微分问题 .证明Tikhonov正则化泛函存在唯一的极小元 ,且这个极小元是一个周期样条 ,并给出了该方法的误差估计 .同其他相关的工作相比 ,发现对周期函数而言 。 The numerical differentiation for the periodic functions is discussed by Tikhonov redularization. It is shown that there exists a unique minimizer for the Tikhonov regularization functional and minimizer is a periodic spline. The error estimate of our method is also given. Compared with other related methods, it gives better approximation on the boundary points. one numerical example is presented .
作者 杨古帆 叶予璋 王盛章
机构地区 复旦大学数学研究所 北海道大学数学系
出处 《复旦学报（自然科学版）》 CAS CSCD 北大核心 2004年第3期315-322,共8页 Journal of Fudan University：Natural Science
关键词 周期函数 数值微分 TIKHONOV正则化 误差估计 周期样条 变分法 ill-posed problems Tikhonov regularization numerical differentiation variation periodic spline
分类号 O241.4 [理学—计算数学]
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参考文献8

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二级参考文献12

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共引文献10

同被引文献36

  • 1王兴华,崔峰.具有最高逼近阶的稳定Lagrange数值微分法[J].中国科学（A辑）,2005,35(11):1314-1320. 被引量：3
  • 2崔丽,秦大同,石万凯.行星齿轮传动啮合效率分析[J].重庆大学学报（自然科学版）,2006,29(3):11-14. 被引量：25
  • 3赵庆华.数值积分校正公式[J].数学的实践与认识,2007,37(9):207-208. 被引量：24
  • 4吴天毅.数值积分中点公式的改进[J].天津理工大学学报,2007,23(3):56-59. 被引量：2
  • 5Wang Y.B. , X.Jia, J. ZandCheng. A numerical differentiation method and its application to reconstruction of discontinuity[J]. Inverse Problems,2002, 18: 1461-1476.
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  • 7Hristian H.Reinsch. Smoothing by Spline Functions Ⅱ[J]. Numer. Math., 1971, 16: 451-454.
  • 8Martin Hanke and Otmar Scherzer. Inverse Problem Light: Numercial Differentiation[J]. THE MATHEMATICAL ASSOCIATION OF AMERICA, 2001, 108: 512-521.
  • 9Huang Jianguo and Chert Yu. A regularization method for the funtion reconstruction from approximate average fluxes[J]. Inverse Problems, 2005, 21: 1667-1684.
  • 10Strang G., Fix G. J. An analysis of the finite element method[M]. NJ: Prentice-Hall, 1973.

引证文献5

二级引证文献10

复旦学报（自然科学版）
2004年 第3期

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