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  - Kirsche, Andreas
A1  - Böckmann, Christine
T1  - Rational approximations for ill-conditioned equation systems
N2  - In this study we present iterative methods using rational approximations, e.g... Pade approximants, which work very well for strongly ill-conditioned systems. In principle all methods of the family are convergent. One type of those methods has the advantage that their convergence behavior is very fast without additional a-priori information on the optimal relaxation parameter. (c) 2005 Elsevier Inc. All rights reserved
Y1  - 2005
ER  - 
TY  - THES
A1  - Kirsche, Andreas
T1  - Regularisierungsverfahren : Entwicklung, Konvergenzuntersuchung und optimale Anpassung für die Fernerkundung
Y1  - 2007
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Böckmann, Christine
A1  - Kirsche, Andreas
T1  - Iterative regularization method for lidar remote sensing
N2  - In this paper we present an inversion algorithm for ill-posed problems arising in atmospheric remote sensing. The proposed method is an iterative Runge-Kutta type regularization method. Those methods are better well known for solving differential equations. We adapted them for solving inverse ill-posed problems. The numerical performances of the algorithm are studied by means of simulations concerning the retrieval of aerosol particle size distributions from lidar observations.
Y1  - 2006
UR  - http://www.sciencedirect.com/science/journal/00104655
U6  - https://doi.org/10.1016/j.cpc.2005.12.019
SN  - 0010-4655
ER  -