New Trends in Parameter Identification for Mathematical Models

✍ Scribed by Bernd Hofmann,Antonio Leitão,Jorge P. Zubelli (eds.)

• Publisher: Birkhäuser Basel
• Year: 2018
• Tongue: English
• Leaves: 347
• Series: Trends in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-viii
Posterior Contraction in Bayesian Inverse Problems Under Gaussian Priors (Sergios Agapiou, Peter Mathé)....Pages 1-29
Convex Regularization of Discrete-Valued Inverse Problems (Christian Clason, Thi Bich Tram Do)....Pages 31-51
Algebraic Reconstruction of Source and Attenuation in SPECT Using First Scattering Measurements (Evelyn Cueva, Axel Osses, Juan Carlos Quintana, Cristián Tejos, Matías Courdurier, Pablo Irarrazaval)....Pages 53-66
On ℓ1-Regularization Under Continuity of the Forward Operator in Weaker Topologies (Daniel Gerth, Bernd Hofmann)....Pages 67-88
On Self-regularization of Ill-Posed Problems in Banach Spaces by Projection Methods (Uno Hämarik, Urve Kangro)....Pages 89-105
Monotonicity-Based Regularization for Phantom Experiment Data in Electrical Impedance Tomography (Bastian Harrach, Mach Nguyet Minh)....Pages 107-120
An SVD in Spherical Surface Wave Tomography (Ralf Hielscher, Daniel Potts, Michael Quellmalz)....Pages 121-144
Numerical Studies of Recovery Chances for a Simplified EIT Problem (Christopher Hofmann, Bernd Hofmann, Roman Unger)....Pages 145-157
Bayesian Updating in the Determination of Forces in Euler-Bernoulli Beams (Alexandre Kawano, Abdelmalek Zine)....Pages 159-174
On Nonstationary Iterated Tikhonov Methods for Ill-Posed Equations in Banach Spaces (M. P. Machado, F. Margotti, Antonio Leitão)....Pages 175-193
The Product Midpoint Rule for Abel-Type Integral Equations of the First Kind with Perturbed Data (Robert Plato)....Pages 195-225
Heuristic Parameter Choice in Tikhonov Method from Minimizers of the Quasi-Optimality Function (Toomas Raus, Uno Hämarik)....Pages 227-244
Modification of Iterative Tikhonov Regularization Motivated by a Problem of Identification of Laser Beam Quality Parameters (Teresa Regińska, Kazimierz Regiński)....Pages 245-259
Tomographic Terahertz Imaging Using Sequential Subspace Optimization (Anne Wald, Thomas Schuster)....Pages 261-290
Adaptivity and Oracle Inequalities in Linear Statistical Inverse Problems: A (Numerical) Survey (Frank Werner)....Pages 291-316
Relaxing Alternating Direction Method of Multipliers (ADMM) for Linear Inverse Problems (Zehui Wu, Shuai Lu)....Pages 317-345

✦ Subjects

Partial Differential Equations