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Taylor series approach for function approximation using ‘estimated’ higher derivatives

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  • Ghosh, Suchismita
  • Deb, Anish
  • Sarkar, Gautam

Abstract

The paper proposes a new approach for function approximation by ‘estimating’ the second derivative, using Taylor series, where the samples of the function and its first derivatives at the sample points are known. Without such ‘estimation’, these initial data, can approximate the function traditionally using the first order Taylor approximation, but with more error. If we desire to improve the approximation via second order Taylor series, then we can estimate the ‘pseudo’ second derivatives of the function in three different ways. All these three ways are investigated in this paper. The pseudo second derivatives help in computing many more sample points of the function within each sampling interval. Thus, the approach acts like a mathematical ‘magnifying glass’. Two examples are treated to compare the efficiencies of the methods. Also, a qualitative study for upper bound of error of the approximations is studied in detail.

Suggested Citation

  • Ghosh, Suchismita & Deb, Anish & Sarkar, Gautam, 2016. "Taylor series approach for function approximation using ‘estimated’ higher derivatives," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 89-101.
  • Handle: RePEc:eee:apmaco:v:284:y:2016:i:c:p:89-101
    DOI: 10.1016/j.amc.2016.02.061
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    References listed on IDEAS

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    1. Dehghan, Mehdi, 2006. "Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 71(1), pages 16-30.
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    Cited by:

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    2. Xie, Qichang & Sun, Qiankun, 2019. "Computation and application of robust data-driven bandwidth selection for gradient function estimation," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 274-293.

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