The TSVD Method for Higher Order Numerical Differentiation of 2D Functions

摘要

Based on the weighted generalized solution regularization theories, we purpose a framework for computing arbitrary order derivatives of bivariate functions when a set of noisy data is given. The convergence results corresponding to the smooth scale of primitive function in Sobolev space are obtained and a concrete algorithm for the first two derivatives is presented in the paper, in which the truncated singular value decomposition (TSVD) is chosen as the needed regularization technique since a singular system of the operator concerned can be derived comparatively easily. Theoretical and numerical results all show that our method is stable and effective.