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Parameter estimation and inverse problems. 2nd ed. (English) Zbl 1273.35306
Amsterdam: Elsevier/Academic Press (ISBN 978-0-12-385048-5/hbk). x, 360 p. (2013).
In this second edition, the authors added some new materials compared to the first edition such as sparsity regularization, compressive sensing and the Markov chain Monte-Carlo method (see [Zbl 1088.35081] for the review of the first edition). Moreover, Chapters 3 and 5 were re-ordered.
The textbook provides a number of examples of parameter estimation problems from different fields which can help motivate students to learn the inverse problem theory. The use of both deterministic and statistical inversion techniques are presented. However, as in the first edition, the theoretical aspects of inverse problems are just briefly discussed and some important inverse problems, especially the partial differental equation-based inverse problems, are omitted.
Table of contents: Chapter 1: Introduction; Chapter 2: Linear regression; Chapter 3: Rank Deficiency and ill-conditioning; Chapter 4: Tikhonov regularization; Chapter 5: Discretizing problems using basic 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; Appendix A: Review of linear algebra; Appendix B: Review of probability and statistics; Appendix C: Review of vector calculus; Appendix D: Glossary of notation.

MSC:
35R30 Inverse problems for PDEs
62F15 Bayesian inference
62J02 General nonlinear regression
62J05 Linear regression; mixed models
35-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations
Software:
GaussFit; Matlab
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