Dept. Math, Hokkaido Univ. EPrints Server

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

Preprint Series # 687
Nakamura, Gen and Wang, Shengzhang and Wang, Yanbo Numerical differentiation of the second order derivative of functions with several variables. (2005);

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Abstract

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.

Item Type:Preprint
Additional Information:20
Uncontrolled Keywords:Numerical differentiation, Regularization, Green function
Subjects:65-xx NUMERICAL ANALYSIS
ID Code:849