Numerical differentiation of the second order derivative of functions with several variables

DOI IR (HANDLE) Open Access

Description

We propose a regularized optimization problem for computing numerical di®erentiation for the second order deriva- tive for functions with two variables from the noisy values of the function at scattered points, and give the proof of the existence and uniqueness of the solution of this problem. The reconstruc- tion scheme is also given during the proof, which is based on bi- harmonic Green function. The convergence estimate of the regular- ized solution to the exact solution for the regularized optimization problem as the regularized parameter and discrepancy of noisy data tending to zero is provided under a simple choice of regularization parameter. In the end we give the numerical examples and analyze the computational results.

Journal

Keywords

Details 詳細情報について

  • CRID
    1390853649725436928
  • NII Article ID
    120006459398
  • DOI
    10.14943/83838
  • HANDLE
    2115/69492
  • Text Lang
    en
  • Article Type
    departmental bulletin paper
  • Data Source
    • JaLC
    • IRDB
    • CiNii Articles
  • Abstract License Flag
    Allowed

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