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近似已知函数求导方法的改进(英文) 被引量：1

IMPROVEMENT OF DIFFERENTIATION OF APPROXIMATELY SPECIFIED FUNCTIONS
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摘要 本文研究了近似已知函数求导方法的改进.利用Lagrange乘数法对罗方法中的系数进行了优化,得到了更快的收敛速度,并给出了相关的数值试验. In this paper we investigate the improvement of numerical differentiation of approximately specified functions.Based on Groetsch’s idea and Luo’s integral operator,we use Lagrange multiplier method to optimize the coefficients in Luo’s method and obtain better convergence rate.Numerical experiments are presented.
作者 王玉洁 王增富
机构地区 吉林大学数学研究所 燕山大学继续教育学院
出处 《数学杂志》 CSCD 北大核心 2012年第6期969-976,共8页 Journal of Mathematics
关键词 收敛速率 不适定问题 数值微分 convergence rate ill-posed problem numerical differentiation
分类号 O241.4 [理学—计算数学]
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  • 1Demigny D. On optimal linear filtering for edge detection[J]. IEEE Transactions on Image Process- ing, 2002, 11(7): 728-737.
  • 2Xu H L, Liu J J. On the Laplacian operation by Lavrentiev regularization with applications in mag- netic resonance electrical impedance tomography[J]. Inverse Problems in Science and Engineering, 2013, 21(2): 251-268.
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  • 4Lu S, Pereverzev S V. Numerical differentiation from a viewpoint of regularization theory[J]. Math. Comput., 2006, 75(256): 1853-1870.
  • 5Zhang Y, Chou Y, Chen J, Zhang Z, Xiao L. Presentation, error analysis and numerical experiments on a group of 1-step-ahead numerical differentiation formulas[J]. J. Comput. Appl. Math., 2013, 239(1): 406-414.
  • 6Wang Y B, Jia X Z, Cheng J. A numerical differentiation method and its application to reconstruc- tion of discontinuity[J]. Inverse Problems, 2002, 18(6): 1461-1476.
  • 7Wei T, Hon Y C, Wang Y B. Reconstruction of numerical derivatives from scattered noisy data[J]. Inverse Problems, 2005, 21(2): 657-672.
  • 8Xu H L, Liu J J. Stable numerical differentiation for the second order derivatives[J]. Adv. Comput. Math., 2010, 33(4): 431-447.
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  • 10Zhao Z Y, Liu J F. Hermite spectral and pseudospectral methods for numerical differentiation[J]. Appl. Numer. Math., 2011, 61(12): 1322-1330.

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数学杂志
2012年 第6期

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