Parameter estimation and inverse problems

Our principal goal for this text continues to be introductory to intermediate level philosophical and methodological understanding of parameter estimation and inverse problems, specifically regarding such key issues as uncertainty, ill-posedness, regularization, bias, and resolution. The accompanying exercises include a mix of applied and theoretical problems. We emphasize key theoretical points and applications with illustrative examples. MATLAB codes and associated data that implement these examples are available in a GitHub repository at We welcome questions, comments, and suggested improvements to the code. The margin icon shown here also indicates where associated code and/or data associated with exercises are available in the repository. This book has necessarily had to distill a tremendous body of mathematics going back to (at least) Newton and Gauss. We hope that it will continue to find a broad audience of students and professionals interested in the general problem of estimating physical models from data. Because this is an introductory text surveying a very broad field, we have not been able to go into great depth. However, each chapter has a “notes and further reading” section to help guide the reader to further exploration of specific topics. Parameter Estimation and Inverse Problems, Third Edition, is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who do not have an extensive mathematical background. The book is complemented by a companion website that includes MATLAB codes that correspond to examples that are illustrated with simple, easy to follow problems that illuminate the details of particular numerical methods. Updates to the new edition include more discussions of Laplacian smoothing, an expansion of basis function exercises, the addition of stochastic descent, an improved presentation of Fourier methods and exercises, and more. Features examples that are illustrated with simple, easy to follow problems that illuminate the details of a particular numerical method Includes an online instructor's guide that helps professors teach and customize exercises and select homework problems Covers updated information on adjoint methods that are presented in an accessible manner