Inverse Problem Theory

Written by: Albert Tarantola (Institut de Physique du Globe de Paris)

Offered freely online as a PDF file, Inverse Problem Theory is an online textbook written by Albert Taratola. Taratola taught at La Sorbonne with the Institut de Physcique du Globe de Paris, Princeton and the University of Santiago de Chile. He passed away in 2009, but we are all fortunate that someone has continued to maintain his site and allow students around the world to access his textbooks and other scholarly papers.

This textbook was written in 2005. It is a total rewrite of an earlier edition published in 1987. The text was written for “all scientists, including applied mathematicians, facing the problem of quantitative interpretation of experimental data in fields such as physics, chemistry, biology, image processing, and information sciences.” It was designed to be used as a reference manual for researchers or as a textbook for undergraduate and graduate students.

If the Preface is similar to the rest of the textbook, it would seem that Taratola explains things well in easy-to-understand language. “Physical theories allow us to make predictions: given a complete description of a physical system, we can predict the outcome of some measurements. This problem of predicting the result of measurements is called the modelization problem, the simulation problem, or the forward problem. The inverse problem consists of using the actual result of some measurements to infer the values of the parameters that characterize the system.”

The problems section of this textbook includes extensive and fully explained answers. That makes this inverse problem theory textbook excellent for self-study or students needing some additional assistance in understanding the material.

Table of Contents for Inverse Problem Theory Textbook

  1. The General Discrete Inverse Problem
  2. Monte Carlo Methods
  3. The Least-Squares Criterion
  4. Least-Absolute-Values Criterion and Minimax Criterion
  5. Functional Inverse Problems
  6. Appendices
  7. Problems

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    Inverse Problem Theory

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