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Explicit Representations for Local Lagrangian Numerical Differentiation

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Abstract

It is shown that in Lagrangian numerical differentiation formulas, the coefficients are explicitly expressed by means of cycle indicator polynomials of symmetric group. Moreover, asymptotic expansions of the remainders are also explicitly represented as a fixed number of interpolation nodes approaching infinitely to the point at which the derivative is evaluated. This implies that complete explicit formulas for local Lagrangian numerical differentiation can be obtained.

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Authors and Affiliations

  1. Computing Center, Zhejiang University, Hangzhou 310012, P. R. China

    He Yu Wang

  2. Department of Mathematics, Hong Kong Baptist University, Hong Kong, P. R. China

    He Yu Wang

  3. Department of Mathematics, Zhejiang University, Hangzhou 310028, P. R. China

    Feng Cui

  4. Department of Mathematics, Zhejiang University, Hangzhou 310028, P. R. China

    Xing Hua Wang

Authors
  1. He Yu Wang
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  2. Feng Cui
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  3. Xing Hua Wang
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Correspondence to Xing Hua Wang.

Additional information

This work is supported in part by the National Natural Science Foundation of China (Grant No. 10471128)

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Wang, H.Y., Cui, F. & Wang, X.H. Explicit Representations for Local Lagrangian Numerical Differentiation. Acta Math Sinica 23, 365–372 (2007). https://doi.org/10.1007/s10114-005-0902-0

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  • DOI: https://doi.org/10.1007/s10114-005-0902-0

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