TY  - JOUR
A1  - Kirsche, Andreas
A1  - Böckmann, Christine
T1  - Pade iteration method for regularization
JF  - Applied mathematics and computation
N2  - In this study we present iterative regularization methods using rational approximations, in particular, Pade approximants, which work well for ill-posed problems. We prove that the (k,j)-Pade method is a convergent and order optimal iterative regularization method in using the discrepancy principle of Morozov. Furthermore, we present a hybrid Pade method, compare it with other well-known methods and found that it is faster than the Landweber method. It is worth mentioning that this study is a completion of the paper [A. Kirsche, C. Bockmann, Rational approximations for ill-conditioned equation systems, Appl. Math. Comput. 171 (2005) 385-397] where this method was treated to solve ill-conditioned equation systems. (c) 2006 Elsevier Inc. All rights reserved.
KW  - Pade approximants
KW  - iterative regularization
KW  - ill-posed problem
Y1  - 2006
U6  - https://doi.org/10.1016/j.amc.2006.01.011
SN  - 0096-3003
VL  - 180
IS  - 2
SP  - 648
EP  - 663
PB  - Elsevier
CY  - New York
ER  - 
TY  - JOUR
A1  - Böckmann, Christine
A1  - Osterloh, Lukas
T1  - Runge-Kutta type regularization method for inversion of spheroidal particle distribution from limited optical data
JF  - Inverse problems in science and engineering
N2  - The Runge-Kutta type regularization method was recently proposed as a potent tool for the iterative solution of nonlinear ill-posed problems. In this paper we analyze the applicability of this regularization method for solving inverse problems arising in atmospheric remote sensing, particularly for the retrieval of spheroidal particle distribution. Our numerical simulations reveal that the Runge-Kutta type regularization method is able to retrieve two-dimensional particle distributions using optical backscatter and extinction coefficient profiles, as well as depolarization information.
KW  - inverse ill-posed problem
KW  - iterative regularization
KW  - integral equation
KW  - laser remote sensing
KW  - inverse scattering
KW  - aerosol size distribution
KW  - 65R32
KW  - 47A52
KW  - 65R20
KW  - 78A46
Y1  - 2014
U6  - https://doi.org/10.1080/17415977.2013.830615
SN  - 1741-5977
SN  - 1741-5985
VL  - 22
IS  - 1
SP  - 150
EP  - 165
PB  - Routledge, Taylor & Francis Group
CY  - Abingdon
ER  -