Parameter estimation and inverse problems
著者
書誌事項
Parameter estimation and inverse problems
（International geophysics series : a series of monographs and textbooks / edited by Renata Dmowska and James R. Holton, 90）
Elsevier Academic Press, c2005
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注記
Includes bibliographical references (p. 283-289) and indexes
内容説明・目次
内容説明
Parameter Estimation and Inverse Problems primarily serves as a textbook for advanced undergraduate and introductory graduate courses. It promotes a fundamental understanding of parameter estimation and inverse problem philosophy and methodology.
It introduces readers to Classical and Bayesian approaches to linear and nonlinear problems, with particular attention to computational, mathematical, and statistical issues related to their application to geophysical problems. Four appendices review foundational concepts in linear algebra, statistics, vector calculus, and notation. Pedagogy includes hundreds of highlighted equations, examples, and definitions; introductory chapter synopses; end-of-chapter exercises, both programming and theoretical; and suggestions for further reading.
The text is designed to be accessible to graduate students and professionals in physical sciences without an extensive mathematical background.
目次
Preface
1. Introduction
2. Linear Regression
3. Discretizing Continuous Inverse Problems
4. Rank Deficiency and Ill-Conditioning
5. Tikhonov Regularization
6. Iterative Methods
7. Other Regularization Techniques
8. Fourier Techniques
9. Nonlinear Regression
10. Nonlinear Inverse Problems
11. Bayesian Methods
Appendix A: Review of Linear Algebra
Appendix B: Review of Probability and Statistics
Appendix C: Glossary of Notation
Bibliography
Index
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