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
- Foundations of Data Science
- 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
In part I we introduced modified Landweber--Kaczmarz methods and
established a convergence analysis. In the present work we
investigate three applications: an inverse problem related to thermoacoustic
tomography, a nonlinear inverse problem for semiconductor equations, and a
nonlinear problem in Schlieren tomography. Each application is
considered in the framework established in the previous part. The
novel algorithms show robustness, stability, computational
efficiency and high accuracy.
IPI
This article is devoted to the convergence analysis of a special family of iterative
regularization methods for solving systems of ill--posed operator equations in Hilbert
spaces, namely Kaczmarz-type methods.
The analysis is focused on the Landweber--Kaczmarz (LK) explicit iteration and the
iterated Tikhonov--Kaczmarz (iTK) implicit iteration. The corresponding symmetric
versions of these iterative methods are also investigated (sLK and siTK).
We prove convergence rates for the four methods above, extending and complementing the
convergence analysis established originally in [22,13,12,8].
IPI
In this article a modified Levenberg-Marquardt method coupled with a Kaczmarz
strategy for obtaining stable solutions of nonlinear systems of ill-posed
operator equations is investigated. We show that the proposed method is a
convergent regularization method. Numerical tests are presented for a non-linear
inverse doping problem based on a bipolar model.
IPI
In this article we develop and analyze novel iterative regularization techniques for
the solution of systems of nonlinear ill-posed operator equations. The basic idea consists
in considering separately each equation of this system and incorporating a loping strategy.
The first technique is a Kaczmarz-type method, equipped with a
novel stopping criteria. The second method is obtained using an embedding strategy,
and again a Kaczmarz-type approach.
We prove well-posedness, stability and convergence of both methods.
IPI
We investigate iterated Tikhonov methods coupled with a Kaczmarz strategy
for obtaining stable solutions of nonlinear systems of ill-posed operator
equations. We show that the proposed method is a convergent regularization
method.
In the case of noisy data we propose a modification, the so called
loping iterated Tikhonov-Kaczmarz method, where a sequence of relaxation
parameters is introduced and a different stopping rule is used. Convergence
analysis for this method is also provided.
Year of publication
Related Authors
Related Keywords
[Back to Top]