Numerical Methods for Inverse Problems
Publication Date: April 2016 Hardback 232 pp.
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.
1. Overview of Inverse Problems.
2. Examples of Inverse Problems.
3. Integral Operators and Integral Equations.
4. Linear Least Squares Problems – Singular Value Decomposition.
5. Regularization of Linear Inverse Problems.
6. Nonlinear Inverse Problems – Generalities.
7. Some Parameter Estimation Examples.
8. Further Information.
About the Authors
Michel Kern is a research scientist in the Serena group at the Inria Research Center in Paris, France