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

✍ Scribed by Gen Nakamura; Shengzhang Wang; Yanbo Wang

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 396 KB
Volume: 212
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2006.11.035

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✦ Synopsis

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.

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