Skip to main content
SpringerLink
Log in

Hermite interpolation and its numerical differentiation formula involving symmetric functions

  • Published:
Applied Mathematics-A Journal of Chinese Universities Aims and scope Submit manuscript

Abstract

By utilizing symmetric functions, this paper presents explicit representations for Hermite interpolation and its numerical differentiation formula. And the corresponding error estimates are also provided.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Li J P. General explicit difference formulas for numerical differentiation, J Comput Appl Math, 2005, 183: 29–52.

    Article  MATH  MathSciNet  Google Scholar 

  2. Khan I R, Ohba R. Closed-form expressions for the finite difference approximations of first and higher derivatives based on Taylor series, J Comput Appl Math, 1999, 107: 179–193.

    Article  MATH  MathSciNet  Google Scholar 

  3. Khan I R, Ohba R. Digital differentiators based on Taylor series, IEICE Trans Fund, 1999, E82-A(12): 2822–2824.

    Google Scholar 

  4. Khan I R, Ohba R. Mathematical proof of explicit formulas for tap-coefficients of Taylor series based FIR difital differentiators, IEICE Trans Fund, 2001, E84-A(6): 1581–1584.

    Google Scholar 

  5. Khan I R, Ohba R. Taylor series based finite difference approximation of high-degree derivatives, J Comput Appl Math, 2003, 154: 115–124.

    Article  MATH  MathSciNet  Google Scholar 

  6. Khan I R, Ohba R, Hozumi N. Mathematical proof of closed form expressions for finite difference approximations based on Taylor series, J Comput Appl Math, 2003, 150: 303–309.

    Article  MATH  MathSciNet  Google Scholar 

  7. Wang X H, Cui F. Stable Lagrangian numerical differentiation with the highest order of approximation, Sci China Ser A, 2006, 49(2): 225–232.

    Article  MATH  MathSciNet  Google Scholar 

  8. Wang H Y, Cui F, Wang X H. Explicit representations for local Lagrangian numerical differentiation, Acta Math Sinica, 2007, 23: 365–372.

    Article  MATH  MathSciNet  Google Scholar 

  9. Comtet L. Advanced Combinatorics, the Art of Finite and Infinite Expansions, Dordrecht: D Reidel Publishing Co, 1974.

    MATH  Google Scholar 

  10. Bai H H, Xu A M, Cui F. Representation for Lagrangian numerical formula involving elementary symmetric functions, J Comput Appl Math, 2009, 231: 907–913.

    Article  MATH  Google Scholar 

  11. Wang X H. On the Hermite interpolation, Sci China Ser A, 2007, 50(11): 1651–1660.

    Article  MATH  MathSciNet  Google Scholar 

  12. Macdonald I G. Symmetric Functions and Hall Polynomials, Second Edition, Oxford: Clarendon Press, 1995.

    MATH  Google Scholar 

  13. Wang X H. The remainder of numerical differentiation formula (in chinese), Hangzhou Daxue Xuebao, 1978, 5(1): 1–10. An announcement of the results appeared in Kexue Tong-bao, 1979, 24: 869–872.

    Google Scholar 

  14. Wang X H, Lai M J, Yang S J. On the divided differences of the remainder in polynomial interpolation, J Approx Theory, 2004, 127: 193–197.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Hong-huan Bai

  2. Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, China

    Ai-min Xu

Authors
  1. Hong-huan Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ai-min Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by the Education Department of Zhejiang Province (Y200806015)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bai, Hh., Xu, Am. Hermite interpolation and its numerical differentiation formula involving symmetric functions. Appl. Math. J. Chin. Univ. 24, 309–314 (2009). https://doi.org/10.1007/s11766-009-2062-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11766-009-2062-y

MR Subject Classification

Keywords

Search

Navigation