A posteriori error analysis for unstable models

作者：Bakushinsky Anatoly B^*; Smirnova Alexandra; Liu Hui

来源：Journal of Inverse and Ill-Posed Problems, 2012, 20(4): 411-428.

DOI：10.1515/jip-2012-0006

• A posteriori error estimate
• nonlinear ill-posed problem
• iterative regularization
• inverse magnetometry problem

In this paper, we consider the possibility of a posteriori error estimates for linear and nonlinear ill-posed operator equations. Given an auxiliary finite-dimensional problem Phi(w) = 0, Phi : D-Phi subset of E-N -%26gt; E-M that approximates the original infinite model F(x) = 0, F : D-F subset of X -%26gt; Y with a certain level of accuracy, we try to estimate the distance between z, an approximate solution to Phi(w) = 0, and x*, the exact solution to F(x) = 0. The problem Phi(w) = 0 is assumed to accumulate different sources of error (discretization, measurements, etc.), and the computed solution z is assumed to satisfy the equation Phi(w) = 0 within a nonzero tolerance delta. We conduct both a theoretical and numerical study of a posteriori error analysis.

• 出版日期2012-10