New Trends in Parameter Identification for Mathematical Models

The Proceedings volume contains 16 contributions to the IMPA conference New Trends in Parameter Identification for Mathematical Models, Rio de Janeiro, Oct 30 Nov 3, 2017, integrating the Chemnitz Symposium on Inverse Problems on Tour. This conference is part of the Thematic Program on Parameter Identification in Mathematical Models organized at IMPA in October and November 2017. One goal is to foster the scientific collaboration between mathematicians and engineers from the Brazialian, European and Asian communities. Main topics are iterative and variational regularization methods in Hilbert and Banach spaces for the stable approximate solution of ill-posed inverse problems, novel methods for parameter identification in partial differential equations, problems of tomography , solution of coupled conduction-radiation problems at high temperatures, and the statistical solution of inverse problems with applications in physics.

Collection of lecture notes, written by experts in the field of inverse problems Contributions present a perspective on the current research trends on selected research topics Fosters the disciplinary and interdisciplinary in Numerical Analysis and Mechanical Engineering

Inhalt
Posterior contraction in Bayesian inverse problems under Gaussian priors.- Convex regularization of discrete-valued inverse problems.- Algebraic reconstruction of source and attenuation in SPECT using first scattering measurements.- On l1-regularization under continuity of the forward operator in weaker topologies.- On self-regularization of ill-posed problems in Banach spaces by projection methods.- Monotonicity-based regularization for phantom experiment data in electrical impedance tomography.- An SVD in Spherical Surface Wave Tomography.- Numerical Studies of Recovery Chances for a Simplified EIT Problem.- Bayesian updating in the determination of forces in Euler-Bernoulli beams.- On nonstationary iterated Tikhonov methods for ill posed equation in Banach spaces.- The product midpoint rule for Abel-type integral equations of the first kind with perturbed data.- Heuristic parameter choice in Tikhonov method form minimizers of the quasi-optimality function.- Modification of Iterative Tikhonov Regularization Motivated by a Problem of Identification of Laser Beam Quality Parameters.- Tomographic terahertz imaging using sequential subspace optimization.- Adaptivity and Oracle Inequalities in Linear Statistical Inverse Problems: a (numerical) survey.- Relaxing Alternating Direction Method of Multipliers (ADMM) algorithm for linear inverse problems.