Numerical differentiation for the second order derivatives of functions of two variables

作者：Nakamura Gen^*; Wang Shengzhang; Wang Yanbo

来源：Journal of Computational and Applied Mathematics, 2008, 212(2): 341-358.

DOI：10.1016/j.cam.2006.11.035

• numerical differentiation
• Tikhonov regularization
• Green's function

A regularized optimization problem for computing numerical differentiation for the second order derivatives of functions with two variables from noisy values at scattered points is discussed in this article. We prove the existence and uniqueness of the solution to this problem, provide a constructive scheme for the solution which is based on bi-harmonic Green's function and give a convergence estimate of the regularized solution to the exact solution for the problem under a simple choice of regularization parameter. The efficiency of the constructive scheme is shown by some numerical examples.

• 出版日期2008-3-1
• 单位复旦大学