Numerical methods for inverse problems

✍ Scribed by Kern, Michel

• Publisher: Wiley-ISTE
• Year: 2016
• Tongue: English
• Leaves: 234
• Edition: 1
• Category: Library

✦ Synopsis

This book studies methods to concretely address inverse problems. An inverse problem arises when the causes that produced a given effect must be determined or when one seeks to indirectly estimate the parameters of a physical system.

The author uses practical examples to illustrate inverse problems in physical sciences. He presents the techniques and specific methods chosen to solve inverse problems in a general domain of application, choosing to focus on a small number of methods that can be used in most applications.

This book is aimed at readers with a mathematical and scientific computing background. Despite this, it is a book with a practical perspective. The methods described are applicable, have been applied, and are often illustrated by numerical examples.

✦ Table of Contents

Content: Introduction and Examples. Overview of Inverse Problems / Michel Kern --
Examples of Inverse Problems / Michel Kern --
Linear Inverse Problems. Integral Operators and Integral Equations / Michel Kern --
Linear Least Squares Problems : Singular Value Decomposition / Michel Kern --
Regularization of Linear Inverse Problems / Michel Kern --
Nonlinear Inverse Problems. Nonlinear Inverse Problems : Generalities / Michel Kern --
Some Parameter Estimation Examples / Michel Kern --
Further Information / Michel Kern --
Appendices. Appendix 1: Numerical Methods for Least Squares Problems --
Appendix 2: Optimization Refreshers --
Appendix 3: Some Results from Functional Analysis.