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© 2018

New Trends in Parameter Identification for Mathematical Models

  • Bernd Hofmann
  • Antonio Leitão
  • Jorge P. Zubelli

Benefits

  • 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

Book

Part of the Trends in Mathematics book series (TM)

Table of contents

  1. Front Matter
    Pages i-viii
    PDF
  2. Posterior Contraction in Bayesian Inverse Problems Under Gaussian Priors
    Sergios Agapiou, Peter Mathé
    Pages 1-29
  3. Convex Regularization of Discrete-Valued Inverse Problems
    Christian Clason, Thi Bich Tram Do
    Pages 31-51
  4. 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
  5. On ℓ1-Regularization Under Continuity of the Forward Operator in Weaker Topologies
    Daniel Gerth, Bernd Hofmann
    Pages 67-88
  6. On Self-regularization of Ill-Posed Problems in Banach Spaces by Projection Methods
    Uno Hämarik, Urve Kangro
    Pages 89-105
  7. Monotonicity-Based Regularization for Phantom Experiment Data in Electrical Impedance Tomography
    Bastian Harrach, Mach Nguyet Minh
    Pages 107-120
  8. An SVD in Spherical Surface Wave Tomography
    Ralf Hielscher, Daniel Potts, Michael Quellmalz
    Pages 121-144
  9. Numerical Studies of Recovery Chances for a Simplified EIT Problem
    Christopher Hofmann, Bernd Hofmann, Roman Unger
    Pages 145-157
  10. Bayesian Updating in the Determination of Forces in Euler-Bernoulli Beams
    Alexandre Kawano, Abdelmalek Zine
    Pages 159-174
  11. On Nonstationary Iterated Tikhonov Methods for Ill-Posed Equations in Banach Spaces
    M. P. Machado, F. Margotti, Antonio Leitão
    Pages 175-193
  12. The Product Midpoint Rule for Abel-Type Integral Equations of the First Kind with Perturbed Data
    Robert Plato
    Pages 195-225
  13. Heuristic Parameter Choice in Tikhonov Method from Minimizers of the Quasi-Optimality Function
    Toomas Raus, Uno Hämarik
    Pages 227-244
  14. Modification of Iterative Tikhonov Regularization Motivated by a Problem of Identification of Laser Beam Quality Parameters
    Teresa Regińska, Kazimierz Regiński
    Pages 245-259
  15. Tomographic Terahertz Imaging Using Sequential Subspace Optimization
    Anne Wald, Thomas Schuster
    Pages 261-290
  16. Adaptivity and Oracle Inequalities in Linear Statistical Inverse Problems: A (Numerical) Survey
    Frank Werner
    Pages 291-316
  17. Relaxing Alternating Direction Method of Multipliers (ADMM) for Linear Inverse Problems
    Zehui Wu, Shuai Lu
    Pages 317-345

About this book

Introduction

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.

Keywords

parameter identification inverse problems ill-posed problems regularization tomography partial differential equations integral equations of the first kind statistical regularization bayesian approach

Editors and affiliations

  • Bernd Hofmann
    • 1
  • Antonio Leitão
    • 2
  • Jorge P. Zubelli
    • 3
  1. 1.Fakultät für MathematikTechnische Universität ChemnitzChemnitzGermany
  2. 2.Department of MathematicsFederal University of Santa CatarinFlorianopolisBrazil
  3. 3.Pura e AplicadaInstituto Nacional de MatematicaRio de JaneiroBrazil

Bibliographic information