Parameter Estimation and Inverse Problems

Richard C. Aster, Brian Borchers and Clifford H. Thurber (Eds.)0120656043, 9780120656042, 9780080470559

Parameter Estimation and Inverse Problems primarily serves as a textbook for advanced undergraduate and introductory graduate courses. Class notes have been developed and reside on the World Wide Web for faciliting use and feedback by teaching colleagues. The authors’ treatment promotes an understanding of fundamental and practical issus associated with parameter fitting and inverse problems including basic theory of inverse problems, statistical issues, computational issues, and an understanding of how to analyze the success and limitations of solutions to these probles. The text is also a practical resource for general students and professional researchers, where techniques and concepts can be readily picked up on a chapter-by-chapter basis. Parameter Estimation and Inverse Problems is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who may not have an extensive mathematical background. It is accompanied by a Web site that contains Matlab code corresponding to all examples. * Designed to be accessible to graduate students and professionals in physical sciences without an extensive mathematical background * Includes three appendices for review of linear algebra and crucial concepts in statistics * Battle-tested in courses at several universities *MATLAB exercises facilitate exploration of material

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Table of contents :
Content:
Preface
Pages xi-xii
Rick Aster, Brian Borchers, Cliff Thurber

1 Introduction
Pages 1-14

2 Linear regression
Pages 15-40

3 Discretizing continuous inverse problems
Pages 41-54

4 Rank deficiency and ill-conditioning
Pages 55-87

5 Tikhonov regularization
Pages 89-118

6 Iterative methods
Pages 119-137

7 Additional regularization techniques
Pages 139-152

8 Fourier techniques
Pages 153-170

9 Nonlinear regression
Pages 171-189

10 Nonlinear inverse problems
Pages 191-200

11 Bayesian methods
Pages 201-217

Appendix A Review of linear algebra
Pages 219-249

Appendix B Review of probability and statistics
Pages 251-272

Appendix C Review of vector calculus
Pages 273-280

Appendix D Glossary of notation
Pages 281-282

Bibliography
Pages 283-289

Index
Pages 291-296