Refine
Year of publication
Document Type
- Article (44)
- Monograph/Edited Volume (6)
- Postprint (6)
- Preprint (6)
- Part of a Book (2)
- Other (2)
- Doctoral Thesis (1)
- Part of Periodical (1)
Keywords
- discrepancy principle (5)
- regularization (5)
- aerosol size distribution (4)
- nonlinear operator (4)
- inverse ill-posed problem (3)
- inversion (3)
- iterative regularization (3)
- logarithmic source condition (3)
- multiwavelength lidar (3)
- 47A52 (2)
Institute
- Institut für Mathematik (52)
- Interdisziplinäres Zentrum für Dynamik komplexer Systeme (6)
- Extern (5)
- Institut für Physik und Astronomie (4)
- Zentrum für Umweltwissenschaften (4)
- Mathematisch-Naturwissenschaftliche Fakultät (3)
- Institut für Umweltwissenschaften und Geographie (1)
- Referat für Presse- und Öffentlichkeitsarbeit (1)
This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under a Holder-type sourcewise condition if the Frechet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt, Lobatto, and Radau methods.
This paper reports on the historical development of the Runge-Kutta methods beginning with the simple Euler method up to an embedded 13-stage method. Moreover, the design and the use of those methods under error order, stability and computation time conditions is edited for students of numerical analysis at undergraduate level. The second part presents applications in natural sciences, compares different methods and illustrates some of the difficulties of numerical solutions.
The Ill-posed Problem of Multiwavelength Lidar Data by a Hybrid Method of Variable Projection
(1999)
The ill-posed inversion of multiwavelength lidar data by a hybrid method of variable projection
(1999)
Strong events of long-range transported biomass burning aerosol were detected during July 2013 at three EARLINET (European Aerosol Research Lidar Network) stations, namely Granada (Spain), Leipzig (Germany) and Warsaw (Poland). Satellite observations from MODIS (Moderate Resolution Imaging Spectroradiometer) and CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarization) instruments, as well as modeling tools such as HYSPLIT (Hybrid Single-Particle Lagrangian Integrated Trajectory) and NAAPS (Navy Aerosol Analysis and Prediction System), have been used to estimate the sources and transport paths of those North American forest fire smoke particles. A multiwavelength Raman lidar technique was applied to obtain vertically resolved particle optical properties, and further inversion of those properties with a regularization algorithm allowed for retrieving microphysical information on the studied particles. The results highlight the presence of smoke layers of 1-2 km thickness, located at about 5 km a.s.l. altitude over Granada and Leipzig and around 2.5 km a.s.l. at Warsaw. These layers were intense, as they accounted for more than 30% of the total AOD (aerosol optical depth) in all cases, and presented optical and microphysical features typical for different aging degrees: color ratio of lidar ratios (LR532/LR355) around 2, alpha-related angstrom exponents of less than 1, effective radii of 0.3 mu m and large values of single scattering albedos (SSA), nearly spectrally independent. The intensive microphysical properties were compared with columnar retrievals form co-located AERONET (Aerosol Robotic Network) stations. The intensity of the layers was also characterized in terms of particle volume concentration, and then an experimental relationship between this magnitude and the particle extinction coefficient was established.
This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under Hölder-type source-wise condition if the Fréchet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt and Radau methods.