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Parameter Estimation and Inverse Problems [Kõva köide]

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(New Mexico Institute of Mining and Technology, Socorro, USA), (University of Wisconsin-Madison, USA), (New Mexico Institute of Mining and Technology, Socorro, USA)
  • Formaat: Hardback, 320 pages, kõrgus x laius: 235x191 mm, kaal: 810 g
  • Ilmumisaeg: 25-Jan-2005
  • Kirjastus: Academic Press Inc
  • ISBN-10: 0120656043
  • ISBN-13: 9780120656042
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Parameter Estimation and Inverse ProblemsSuurem pilt
  • Formaat: Hardback, 320 pages, kõrgus x laius: 235x191 mm, kaal: 810 g
  • Ilmumisaeg: 25-Jan-2005
  • Kirjastus: Academic Press Inc
  • ISBN-10: 0120656043
  • ISBN-13: 9780120656042
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780120656042.html
Märksõnad:
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

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

Arvustused

"...a very useful textbook at undergraduate and graduate-level courses teaching the numerical techniques used in parameter estimation...it will certainly be a very useful reference also for practitioners who need a guide in selecting the proper mathematical approach when solving real problems, not only in geophysics, but also other branches of science and engineering." --Wojciech Debski, Institute of Geophysics, Polish Academy of Sciences

"The great strength of this book is that it is a 'one-shop-stop' for solving inverse problems; it contains many different methods for solving your particular problems and, in general, all of the background mathematics to help you understand the method itself." --John Brittan, in THE LEADING EDGE, SEPT 2005

"The writing is uniformly clear; one unfamiliar with even the most basic ideas of inverse theory will find it ideal for self-study. ...I found the authors treatment of such concepts as existence, uniqueness, instability, resolution, and ill-posedness to be particularly succinct. They do a fine job in distinguishing the continuous from the discrete case, and they point out some of the pitfalls that can arise when going from one to the other, yet without becoming bogged down in sterile mathematical detail. ...This is an exceptionally well written introductory text which, for a change, is reasonably priced, placing it at least within reach of a college student." --Sven Treitel, The Leading Edge, March 2006

This is a well designed textbook with a very clean approach [ and] a fine introduction for inverse problems in applied fields. The tone of the writing is conversational in a way that allows the ideas to come across clearly, while the content is mathematically rigorous, presenting details relevent to the topic and providing references for the rest. --Paul Phillips, University of Dallas for MAA, February 2006

"A well-presented textbook [ and] a one-stop-shop for solving inverse problems...a well recommended addition to the technical library of anybody who has to deal with inverse problems on a regular basis." --John Brittan, Walton-on-Thames, UK for "The Leading Edge", September 2005

Muu info

* 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
Preface xi
Introduction
1(14)
Classification of Inverse Problems
1(3)
Examples of Parameter Estimation Problems
4(3)
Examples of Inverse Problems
7(4)
Why Inverse Problems Are Hard
11(3)
Exercises
14(1)
Notes and Further Reading
14(1)
Linear Regression
15(26)
Introduction to Linear Regression
15(2)
Statistical Aspects of Least Squares
17(9)
Unknown Measurement Standard Deviations
26(4)
L1 Regression
30(5)
Monte Carlo Error Propagation
35(1)
Exercises
36(4)
Notes and Further Reading
40(1)
Discretizing Continuous Inverse Problems
41(14)
Integral Equations
41(1)
Quadrature Methods
41(5)
Expansion in Terms of Representers
46(1)
Expansion in Terms of Orthonormal Basis Functions
47(1)
The Method of Backus and Gilbert
48(4)
Exercises
52(2)
Notes and Further Reading
54(1)
Rank Deficiency and Ill-Conditioning
55(34)
The SVD and the Generalized Inverse
55(7)
Covariance and Resolution of the Generalized Inverse Solution
62(2)
Instability of the Generalized Inverse Solution
64(3)
An Example of a Rank-Deficient Problem
67(6)
Discrete Ill-Posed Problems
73(12)
Exercises
85(2)
Notes and Further Reading
87(2)
Tikhonov Regularization
89(30)
Selecting a Good Solution
89(2)
SVD Implementation of Tikhonov Regularization
91(4)
Resolution, Bias, and Uncertainty in the Tikhonov Solution
95(3)
Higher-Order Tikhonov Regularization
98(5)
Resolution in Higher-Order Tikhonov Regularization
103(2)
The TGSVD Method
105(1)
Generalized Cross Validation
106(3)
Error Bounds
109(5)
Exercises
114(3)
Notes and Further Reading
117(2)
Iterative Methods
119(20)
Introduction
119(1)
Iterative Methods for Tomography Problems
120(6)
The Conjugate Gradient Method
126(5)
The CGLS Method
131(4)
Exercises
135(1)
Notes and Further Reading
136(3)
Additional Regularization Techniques
139(14)
Using Bounds as Constraints
139(4)
Maximum Entropy Regularization
143(3)
Total Variation
146(5)
Exercises
151(1)
Notes and Further Reading
152(1)
Fourier Techniques
153(18)
Linear Systems in the Time and Frequency Domains
153(5)
Deconvolution from a Fourier Perspective
158(3)
Linear Systems in Discrete Time
161(3)
Water Level Regularization
164(4)
Exercises
168(2)
Notes and Further Reading
170(1)
Nonlinear Regression
171(20)
Newton's Method
171(3)
The Gauss-Newton and Levenberg-Marquardt Methods
174(3)
Statistical Aspects
177(4)
Implementation Issues
181(5)
Exercises
186(3)
Notes and Further Reading
189(2)
Nonlinear Inverse Problems
191(10)
Regularizing Nonlinear Least Squares Problems
191(4)
Occam's Inversion
195(4)
Exercises
199(1)
Notes and Further Reading
199(2)
Bayesian Methods
201(18)
Review of the Classical Approach
201(1)
The Bayesian Approach
202(5)
The Multivariate Normal Case
207(5)
Maximum Entropy Methods
212(2)
Epilogue
214(2)
Exercises
216(1)
Notes and Further Reading
217(2)
A REVIEW OF LINEAR ALGEBRA
219(32)
A.1 Systems of Linear Equations
219(3)
A.2 Matrix and Vector Algebra
222(6)
A.3 Linear Independence
228(1)
A.4 Subspaces of Rn
229(4)
A.5 Orthogonality and the Dot Product
233(4)
A.6 Eigenvalues and Eigenvectors
237(3)
A.7 Vector and Matrix Norms
240(2)
A.8 The Condition Number of a Linear System
242(2)
A.9 The QR Factorization
244(1)
A.10 Linear Algebra in Spaces of Functions
245(2)
A.11 Exercises
247(2)
A.12 Notes and Further Reading
249(2)
B REVIEW OF PROBABILITY AND STATISTICS
251(22)
B.1 Probability and Random Variables
251(6)
B.2 Expected Value and Variance
257(1)
B.3 Joint Distributions
258(4)
B.4 Conditional Probability
262(2)
B.5 The Multivariate Normal Distribution
264(1)
B.6 The Central Limit Theorem
265(1)
B.7 Testing for Normality
265(2)
B.8 Estimating Means and Confidence Intervals
267(2)
B.9 Hypothesis Tests
269(2)
B.10 Exercises
271(1)
B.11 Notes and Further Reading
272(1)
C REVIEW OF VECTOR CALCULUS
273(8)
C.1 The Gradient, Hessian, and Jacobian
273(2)
C.2 Taylor's Theorem
275(1)
C.3 Lagrange Multipliers
276(2)
C.4 Exercises
278(2)
C.5 Notes and Further Reading
280(1)
D GLOSSARY OF NOTATION
281(2)
Bibliography 283(8)
Index 291
Professor Aster is an Earth scientist with broad interests in geophysics, seismological imaging and source studies, and Earth processes. His work has included significant field research in western North America, Italy, and Antarctica. Professor Aster also has strong teaching and research interests in geophysical inverse and signal processing methods and is the lead author on the previous two editions. Aster was on the Seismological Society of America Board of Directors, 2008-2014 and won the IRIS Leadership Award, 2014. Dr. Borchers primary research and teaching interests are in optimization and inverse problems. He teaches a number of undergraduate and graduate courses at NMT in linear programming, nonlinear programming, time series analysis, and geophysical inverse problems. Dr. Borchers research has focused on interior point methods for linear and semidefinite programming and applications of these techniques to combinatorial optimization problems. He has also done work on inverse problems in geophysics and hydrology using linear and nonlinear least squares and Tikhonov regularization. Professor Thurber is an international leader in research on three-dimensional seismic imaging ("seismic tomography") using earthquakes. His primary research interests are in the application of seismic tomography to fault zones, volcanoes, and subduction zones, with a long-term focus on the San Andreas fault in central California and volcanoes in Hawaii and Alaska. Other areas of expertise include earthquake location (the topic of a book he edited) and geophysical inverse theory.