Numerical Methods for Inverse Problems

✍ Scribed by Olga Moreira (editor)

• Publisher: Arcler Press
• Year: 2020
• Tongue: English
• Leaves: 346
• Category: Library

✦ Synopsis

The book "Numerical Methods for Inverse Problems" consists of contemporaneouss articles featuring not only several well-known inverse problems used in the inference of many physical and engineering systems such as that of the partial differential equations but also the statistical and imaging inverse problems. It includes a variety of numerical methods for solving inverse problems such as that of the Tikhonov regularization; finite differences; and orthogonal decomposition; as well as those based on Bayesian inference, artificial neural networks, and quantum annealing.

✦ Table of Contents

Cover
Title Page
Copyright
DECLARATION
ABOUT THE EDITOR
TABLE OF CONTENTS
List of Contributors
List of Abbreviations
Preface
Chapter 1 A Numerical Approximation Method for the Inverse Problem of the Three-Dimensional Laplace Equation
Abstract
Introduction
Mathematical Problem And The Ill-Posedness Analysis
Mollification Method And Regularization Solution
Parameter Selection And Error Estimates
Numerical Examples
Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts Of Interest
References
Chapter 2 The Numerical Solution of Forward and Inverse Robin Problems for Laplace’s Equation
Abstract
Introduction
Fast Solution Of The Forward Problem
The Robin Inverse Problem And Preconditioner
Numerical Examples
Acknowledgements
Funding
Contributions
References
Chapter 3 Moving Least Squares Method for a One-dimensional Parabolic Inverse Problem
Abstract
Introduction
An Outline Of The Moving Least Squares (Mls)
The Inverse Problem And Its Numerical Solution
Numerical Experiments And Discussions
Conclusion
Conflict Of Interests
Acknowledgments
References
Chapter 4 The Inverse Problem of the Heat Equation with Periodic Boundary And Integral Overdetermination Conditions
Abstract
Introduction
Existence And Uniqueness Of The Solution Of The Inverse Problem
Continuous Dependence Of (P,U) Upon The Data
Numerical Method
Numerical Example And Discussions
Conclusions
Acknowledgements
References
Chapter 5 An Inverse Problem for a Two-Dimensional Time- Fractional Sideways Heat Equation
Abstract
Introduction
Description Of The 2D Time-Fractional Inverse Diffusion Problem
A Modified Method And Convergence Estimates
Numerical Aspect
Conclusion
Data Availability
Conflicts Of Interest
Authors’ Contributions
Acknowledgments
References
Chapter 6 Numerical Inversion for the Multiple Fractional Orders in the Multiterm TFDE
Abstract
Introduction
The Forward Problem And The Inverse Problem
The Inversion Algorithm And Numerical Inversions
Conclusions
Conflicts Of Interest
Acknowledgments
References
Chapter 7 Solutions of Direct and Inverse Even-Order Sturm- Liouville Problems Using Magnus Expansion
Abstract
Introduction
Materials And Methods
Results Of Direct Sturm–Liouville Problems
Results Of Inverse Sturm–Liouville Problems
Discussion And Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts Of Interest
Abbreviations
Appendix A
References
Chapter 8 Numerical Solution of Direct and Inverse Problems for Time-Dependent Volterra Integro-Differential Equation Using Finite Integration Method with Shifted Chebyshev Polynomials
Abstract
Introduction
Preliminaries
Numerical Algorithms For Direct And Inverse Problems Of Tvide
Numerical Experiments
Conclusions And Discussion
Author Contributions
Acknowledgments
Conflicts Of Interest
Abbreviations
References
Chapter 9 Direct and Inverse Problem for Geometric Perturbation of the Laplace Operator in a Strip
Abstract
Introduction
The Direct Problem
The Inverse Problem
Conclusion
Appendices
Acknowledgements
Contributions
References
Chapter 10 Solving Large-Scale Inverse Magnetostatic Problems Using the Adjoint Method
Abstract
Introduction
Adjoint Method
Numerical Experiments
Conclusion
Acknowledgements
Contributions
References
Chapter 11 The Problem of the Inverse Lyapunov Exponent and its Applications
Abstract
Introduction
Formulation Of The Problem
Results
Example
Applications
Conclusions
References
Chapter 12 Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach
Abstract
Introduction
Mathematical Description
Nonlinear Damping Identification
Stochastic Inverse Formalism
Hierarchical Bayesian Formulation
Posterior State Exploration
Numerical Experiments
A Particular Application To Realistic Problem: Ship Roll Motion
Conclusions
References
Chapter 13 Model Order Reduction for Bayesian Approach to Inverse Problems
Abstract
Background
Methods
Results And Discussion
Conclusion
References
Chapter 14 Statistical Approaches to the Inverse Problem
Introduction
Statistics And Inverse Problems
Basic Facts About The Meg Inverse Problem
Imaging Methods
Parametric Methods
Highly Automated Dipole Estimation
Hades
Conclusion
Acknowledgements
References
Index
Back Cover