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E-raamat: Parameter Estimation and Inverse Problems

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(University of Wisconsin-Madison, USA), (New Mexico Institute of Mining and Technology, Socorro, USA), (New Mexico Institute of Mining and Technology, Socorro, USA)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 16-Oct-2018
  • Kirjastus: Elsevier Science Publishing Co Inc
  • Keel: eng
  • ISBN-13: 9780128134238
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Parameter Estimation and Inverse ProblemsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 16-Oct-2018
  • Kirjastus: Elsevier Science Publishing Co Inc
  • Keel: eng
  • ISBN-13: 9780128134238
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Parameter Estimation and Inverse Problems, Third Edition, is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who do not have an extensive mathematical background. The book is complemented by a companion website that includes MATLAB codes that correspond to examples that are illustrated with simple, easy to follow problems that illuminate the details of particular numerical methods. Updates to the new edition include more discussions of Laplacian smoothing, an expansion of basis function exercises, the addition of stochastic descent, an improved presentation of Fourier methods and exercises, and more.

  • Complemented by a companion website that includes MATLAB codes that correspond to all examples
  • Features examples that are illustrated with simple, easy to follow problems that illuminate the details of a particular numerical method
  • Includes an online instructor’s guide that helps professors teach and customize exercises and select homework problems
  • Covers updated information on adjoint methods that are presented in an accessible manner
Preface to the Third Edition ix
1 Introduction
1(24)
1.1 Classification of Parameter Estimation and Inverse Problems
1(3)
1.2 Examples of Parameter Estimation Problems
4(4)
1.3 Examples of Inverse Problems
8(5)
1.4 Discretizing Integral Equations
13(5)
1.5 Why Inverse Problems Are Hard
18(3)
1.6 Exercises
21(1)
1.7 Notes and Further Reading
22(3)
2 Linear Regression
25(30)
2.1 Introduction to Linear Regression
25(2)
2.2 Statistical Aspects of Least Squares
27(10)
2.3 An Alternative View of the 95% Confidence Ellipsoid
37(2)
2.4 Unknown Measurement Standard Deviations
39(4)
2.5 L1 Regression
43(5)
2.6 Monte Carlo Error Propagation
48(1)
2.7 Exercises
49(4)
2.8 Notes and Further Reading
53(2)
3 Rank Deficiency and Ill-Conditioning
55(9)
3.1 The SVD and the Generalized Inverse
55(6)
3.2 Covariance and Resolution of the Generalized Inverse Solution
61(3)
33 Instability of the Generalized Inverse Solution
64(29)
3.4 A Rank Deficient Tomography Problem
67(7)
3.5 Discrete Ill-Posed Problems
74(14)
3.6 Exercises
88(3)
3.7 Notes and Further Reading
91(2)
4 Tikhonov Regularization
93(42)
4.1 Selecting a Good Solution
93(2)
4.2 SVD Implementation of Tikhonov Regularization
95(5)
4.3 Resolution, Bias, and Uncertainty in the Tikhonov Solution
100(3)
4.4 Higher-Order Tikhonov Regularization
103(8)
4.5 Resolution in Higher-Order Tikhonov Regularization
111(2)
4.6 The TGSVD Method
113(3)
4.7 Generalized Cross-Validation
116(4)
4.8 Error Bounds
120(5)
4.9 Using Bounds as Constraints
125(5)
4.10 Exercises
130(3)
4.11 Notes and Further Reading
133(2)
5 Discretizing Inverse Problems Using Basis Functions
135(16)
5.1 Discretization by Expansion of the Model
135(5)
5.2 Using Representers as Basis Functions
140(1)
5.3 Reformulation in Terms of an Orthonormal Basis
141(2)
5.4 The Method of Backus and Gilbert
143(4)
5.5 Exercises
147(1)
5.6 Notes and Further Reading
148(3)
6 Iterative Methods
151(30)
6.1 Introduction
151(1)
6.2 Row Action Methods for Tomography Problems
152(4)
6.3 The Gradient Descent Method
156(4)
6.4 The Conjugate Gradient Method
160(5)
6.5 The CGLS Method
165(5)
6.6 Resolution Analysis for Iterative Methods
170(6)
6.7 Exercises
176(3)
6.8 Notes and Further Reading
179(2)
7 Sparsity Regularization and Total Variation Techniques
181(30)
7.1 Sparsity Regularization
181(1)
7.2 The Iterative Soft Threshholding Algorithm (ISTA)
182(7)
7.3 Sparse Representation and Compressive Sensing
189(6)
7.4 Total Variation Regularization
195(1)
7.5 Using IRLS to Solve L1 Regularized Problems
196(2)
7.6 The Alternating Direction Method of Multipliers (ADMM)
198(7)
7.7 Total Variation Image Denoising
205(3)
7.8 Exercises
208(1)
7.9 Notes and Further Reading
209(2)
8 Fourier Techniques
211(24)
8.1 Linear Systems in the Time and Frequency Domains
211(6)
8.2 Linear Systems in Discrete Time
217(4)
8.3 Water Level Regularization
221(4)
8.4 Tikhonov Regularization in the Frequency Domain
225(5)
8.5 Exercises
230(3)
8.6 Notes and Further Reading
233(2)
9 Nonlinear Regression
235(22)
9.1 Introduction to Nonlinear Regression
235(1)
9.2 Newton's Method for Solving Nonlinear Equations
235(3)
9.3 The Gauss-Newton and Levenberg-Marquardt Methods for Solving Nonlinear Least Squares Problems
238(3)
9.4 Statistical Aspects of Nonlinear Least Squares
241(5)
9.5 Implementation Issues
246(6)
9.6 Exercises
252(3)
9.7 Notes and Further Reading
255(2)
10 Nonlinear Inverse Problems
257(22)
10.1 Regularizing Nonlinear Least Squares Problems
257(5)
10.2 Occam's Inversion
262(4)
10.3 Model Resolution in Nonlinear Inverse Problems
266(3)
10.4 The Nonlinear Conjugate Gradient Method
269(1)
10.5 The Discrete Adjoi nt Method 2
270(6)
10.6 Exercises
276(1)
10.7 Notes and Further Reading
277(2)
11 Bayesian Methods
279(28)
11.1 Review of the Classical Approach
279(2)
11.2 The Bayesian Approach
281(5)
11.3 The Multivariate Normal Case
286(9)
11.4 The Markov Chain Monte Carlo (MCMC) Method
295(4)
11.5 Analyzing MCMC Output
299(4)
11.6 Exercises
303(2)
11.7 Notes and Further Reading
305(2)
12 Epilogue
307(2)
A Review of Linear Algebra
309(32)
A.1 Systems of Linear Equations
309(3)
A.2 Matrix and Vector Algebra
312(6)
A.3 Linear Independence
318(1)
A.4 Subspacesofi?
319(5)
A.5 Orthogonality and the Dot Product
324(4)
A.6 Eigenvalues and Eigenvectors
328(2)
A.7 Vector and Matrix Norms
330(2)
A.8 The Condition Number of a Linear System
332(2)
A.9 The QR Factorization
334(2)
A.10 Complex Matrices and Vectors
336(1)
A.11 Linear Algebra in Spaces of Functions
337(1)
A.12 Exercises
338(2)
A.13 Notes and Further Reading
340(1)
B Review of Probability and Statistics
341(22)
B.1 Probability and Random Variables
341(6)
B.2 Expected Value and Variance
347(1)
B.3 Joint Distributions
348(4)
B.4 Conditional Probability
352(2)
B.5 The Multivariate Normal Distribution
354(1)
B.6 The Central Limit Theorem
355(1)
B.7 Testing for Normality
356(2)
B.8 Estimating Means and Confidence Intervals
358(2)
B.9 Exercises
360(1)
B.10 Notes and Further Reading
361(2)
C Review of Vector Calculus
363(8)
C.1 The Gradient, Hessian, and Jacobian
363(1)
C.2 Taylor's Theorem
364(1)
C.3 Lagrange Multipliers
365(3)
C.4 Exercises
368(1)
C.5 Notes and Further Reading
369(2)
D Glossary of Notation
371(2)
Bibliography 373(10)
Index 383
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.
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