### Table of Contents

Preface.

Chapter 1: Introduction.

Chapter 2: Linear Regression.

Chapter 3: Rank Deficiency and Ill Conditioning.

Chapter 4: Tikhonov Regularization.

Chapter 5: Discretizing Inverse Problems Using Basis Functions.

Chapter 6: Iterative Methods.

Chapter 7: Additional Regularization Techniques.

Chapter 8: Fourier Techniques.

Chapter 9: Nonlinear Regression.

Chapter 10: Nonlinear Inverse Problems.

Chapter 11: Bayesian Methods.

Chapter 12: Epilogue.

A. Review of Linear Algebra.

B. Review of Probability and Statistics.

C. Review of Vector Calculus.

D. Glossary of Notation.

Bibliography.

Index. Parameter Estimation and Inverse Problems, 2e provides geoscience students and professionals with answers to common questions like how one can derive a physical model from a finite set of observations containing errors, and how one may determine the quality of such a model. This book takes on these fundamental and challenging problems, introducing students and professionals to the broad range of approaches that lie in the realm of inverse theory. The authors present both the underlying theory and practical algorithms for solving inverse problems. The authors' treatment is appropriate for geoscience graduate students and advanced undergraduates with a basic working knowledge of calculus, linear algebra, and statistics. Parameter Estimation and Inverse Problems, 2e introduces readers to both Classical and Bayesian approaches to linear and nonlinear problems with particular attention paid to computational, mathematical, and statistical issues related to their application to geophysical problems. The textbook includes Appendices covering essential linear algebra, statistics, and notation in the context of the subject. A companion website features computational examples (including all examples contained in the textbook) and useful subroutines using MATLAB. Includes appendices for review of needed concepts in linear, statistics, and vector calculus. Companion website contains comprehensive MATLAB code for all examples, which readers can reproduce, experiment with, and modify. Online instructor's guide helps professors teach, customize exercises, and select homework problems Accessible to students and professionals without a highly specialized mathematical background.

Chapter 1: Introduction.

Chapter 2: Linear Regression.

Chapter 3: Rank Deficiency and Ill Conditioning.

Chapter 4: Tikhonov Regularization.

Chapter 5: Discretizing Inverse Problems Using Basis Functions.

Chapter 6: Iterative Methods.

Chapter 7: Additional Regularization Techniques.

Chapter 8: Fourier Techniques.

Chapter 9: Nonlinear Regression.

Chapter 10: Nonlinear Inverse Problems.

Chapter 11: Bayesian Methods.

Chapter 12: Epilogue.

A. Review of Linear Algebra.

B. Review of Probability and Statistics.

C. Review of Vector Calculus.

D. Glossary of Notation.

Bibliography.

Index. Parameter Estimation and Inverse Problems, 2e provides geoscience students and professionals with answers to common questions like how one can derive a physical model from a finite set of observations containing errors, and how one may determine the quality of such a model. This book takes on these fundamental and challenging problems, introducing students and professionals to the broad range of approaches that lie in the realm of inverse theory. The authors present both the underlying theory and practical algorithms for solving inverse problems. The authors' treatment is appropriate for geoscience graduate students and advanced undergraduates with a basic working knowledge of calculus, linear algebra, and statistics. Parameter Estimation and Inverse Problems, 2e introduces readers to both Classical and Bayesian approaches to linear and nonlinear problems with particular attention paid to computational, mathematical, and statistical issues related to their application to geophysical problems. The textbook includes Appendices covering essential linear algebra, statistics, and notation in the context of the subject. A companion website features computational examples (including all examples contained in the textbook) and useful subroutines using MATLAB. Includes appendices for review of needed concepts in linear, statistics, and vector calculus. Companion website contains comprehensive MATLAB code for all examples, which readers can reproduce, experiment with, and modify. Online instructor's guide helps professors teach, customize exercises, and select homework problems Accessible to students and professionals without a highly specialized mathematical background.

Aster, Richard C;Borchers, Brian;Thurber, Clifford H

- Academic Press

2013

2nd ed.

9780123850485

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