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A posteriori error analysis for unstable models
-
Anatoly B. Bakushinsky
,
Alexandra Smirnova
Published/Copyright:
October 2, 2012
Abstract.
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 
, 
that approximates the original infinite model 
, 
with a certain level of accuracy,
we try to estimate the distance between z, an approximate solution to , and 
, the exact solution to . The problem
is assumed to accumulate different sources of error (discretization, measurements, etc.), and the computed solution z is assumed to satisfy the equation
within a nonzero tolerance 
.
We conduct both a theoretical and numerical study of a posteriori error analysis.
Keywords: A posteriori error estimate; nonlinear ill-posed problem; iterative regularization; inverse magnetometry problem
Received: 2012-02-01
Published Online: 2012-10-02
Published in Print: 2012-10-01
© 2012 by Walter de Gruyter Berlin Boston
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Keywords for this article
A posteriori error estimate;
nonlinear ill-posed problem;
iterative regularization;
inverse magnetometry problem
Articles in the same Issue
- Masthead
- Preface
- Single-logarithmic stability for the Calderón problem with local data
- The identification problem for the functional equation with a parameter
- A posteriori error analysis for unstable models
- A review of selected techniques in inverse problem nonparametric probability distribution estimation
- Unified approach to classical equations of inverse problem theory
- Optimized analytic reconstruction for SPECT
- Numerical method for solving an inverse electrocardiography problem for a quasi stationary case
- A new approximate mathematical model for global convergence for a coefficient inverse problem with backscattering data
- On inverse problems in partially ordered spaces with a priori information
- An iterative method for a two-dimensional inverse scattering problem for a dielectric
- On the Shack–Hartmann based wavefront reconstruction: Stability and convergence rates of finite-dimensional approximations
- Unique continuation and continuous dependence results for a severely ill-posed integro-differential parabolic problem
