## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

IPI

Inverse problems are known to be very intolerant to both data errors
and errors in the forward model.
With several inverse problems the adequately accurate forward model can turn out to be
computationally excessively complex.
The Bayesian framework for inverse problems has recently been shown to enable
the adoption of highly approximate forward models.
This approach is based on the modelling of the associated approximation errors
that are incorporated in the construction of the computational model.
In this paper we investigate the extension of the approximation error theory to
nonstationary inverse problems.
We develop the basic framework for linear nonstationary inverse problems
that allows one to use both highly reduced states and extended time steps.
As an example we study the one dimensional heat equation.

IPI

Numerical realization of mathematical models always induces errors
to the computational models, thus affecting both predictive
simulations and related inversion results. Especially, inverse
problems are typically sensitive to modeling and measurement errors,
and therefore the accuracy of the numerical model is a crucial issue
in inverse computations. For instance, in problems related to
partial differential equation models, the implementation of a
numerical model with high accuracy necessitates the use of fine
discretization and realistic boundary conditions. However, in some
cases realistic boundary conditions can be posed only for very large
or even unbounded computational domains. Fine discretization and
large domains lead to very high-dimensional models that may be of
prohibitive computational cost.
Therefore, it
is often necessary in practice to use coarser discretization and
smaller computational domains with more or less incorrect
boundary conditions in order to decrease the dimensionality of the model.
In this paper we apply the recently proposed approximation error approach
to the problem of incorrectly posed boundary conditions.
As a specific computational example we consider the imaging of conductivity
distribution of soil using electrical resistance tomography.
We show that the approximation error approach can also be applied to domain truncation
problems and that it allows one to use significantly smaller scale
forward models in the inversion.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]