Inverse Problem Theory and Model Parameter Estimation eBook description :
Description
The first part of this book deals exclusively with discrete inverse problems with a finite number of parameters. Some real problems are naturally discrete, while others contain functions of a continuous variable and can be discretized if the functions under consideration are smooth enough compared to the sampling length, or if the functions can conveniently be described by their development on a truncated basis. The advantage of a discretized point of view for problems involving functions is that the mathematics is easier. The disadvantage is that some simplifications arising in a general approach can be hidden when using a discrete formulation. (Discretizing the forward problem and setting a discrete inverse problem is not always equivalent to setting a general inverse problem and discretizing for the practical computations.)
The second part of the book deals with general inverse problems, which may contain such functions as data or unknowns. As this general approach contains the discrete case in particular, the separation into two parts corresponds only to a didactical purpose.
Although this book contains a lot of mathematics, it is not a mathematical book. It tries to explain how a method of acquisition of information can be applied to the actual world, and many of the arguments are heuristic.
Contents
The General Discrete Inverse Problem
Monte Carlo Methods
The Least-Squares Criterion
Least-Absolute-Values Criterion and Minimax Criterion
Functional Inverse Problems
Book Details
Author(s): Albert Tarantola
Format(s): PDF
File size: 20.08 MB
Number of pages: 358
