国外数学名著系列（续一影印版）40：模型参数估计的反问题理论与方法
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作者： （意）塔兰托拉 著
出 版 社： 科学出版社
出版时间： 2009-1-1字数： 431000版次： 1页数： 342印刷时间： 2009/01/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9787030234841包装： 精装内容简介
Prompted by recent developments in inverse theory, Inverse Problem Theory and Methods for Model Parameter Estimation is a completely rewritten version of a 1987 book by the same author. In this version there are many algorithmic details for Monte Carlo methods, leastsquares discrete problems, and least-squares problems involving functions. In addition, some notions are clarified, the role of optimization techniques is underplayed, and Monte Carlo methods are taken much more seriously. The first part of the book deals exclusively with discrete inverse problems with afinite number of parameters, while the second part of the book deals with general inverse problems. ...
目录
Preface
1 The General Discrete Inverse Problem
1.1 Model Space and Data Space
1.2 States of Information
1.3 Forward Problem
1.4 Measurements and A Priori Information
1.5 Defining the Solution of the Inverse Problem
1.6 Using the Solution of the Inverse Problem
2 Monte Carlo Methods
2.1 Introduction
2.2 The Movie Strategy for Inverse Problems
2.3 Sampling Methods
2.4 Monte Carlo Solution to Inverse Problems
2.5 Simulated Annealing
3 The Least-Squares Criterion
3.1 Preamble: The Mathematics of Linear Spaces
3.2 The Least-Squares Problem
3.3 Estimating Posterior Uncertainties
3.4 Least-Squares Gradient and Hessian
4 Least-Absolute-Values Criterion and Minimax Criterion
4.1 Introduction
4.2 Preamble:ln-Norms
4.3 The ln-Norm Problem
4.4 The l1-Norm Criterion for Inverse Problems
4.5 The ln-Norm Criterion for Inverse Problems
5 Functional Inverse Problems
5.1 Random Functions
5.2 Solution of General Inverse Problems
5.3 Introduction to Functional Least Squares
5.4 Derivative and Transpose Operators in Functional Spaces
5.5 General Least-Squares Inversion
5.6 Example: X-Ray Tomography as an Inverse Problem
5.7 Example: Travel-Time Tomography
5.8 Example: Nonlinear Inversion of Elastic Waveforms
6 Appendices
6.1 Volumetric Probability and Probability Density
6.2 Homogeneous Probability Distributions
6.3 Homogeneous Distribution for Elastic Parameters
6.4 Homogeneous Distribution for Second-Rank Tensors
6.5 Central Estimators and Estimators of Dispersion
6.6 Generalized Gaussian
6.7 Log-Normal Probability Density
6.8 Chi-Squared Probability Density
6.9 Monte Carlo Method of Numerical Integration
6.10Sequential Random Realization
6.11Cascaded Metropolis Algorithm
6.12Distance and Norm
6.13The Different Meanings of the Word Kernel
6.14Transpose and Adjoint of a Differential Operator
6.15The Bayesian Viewpoint of Backus (1970)
6.16The Method of Backus and Gilbert
6.17Disjunction and Conjunction of Probabilities
6.18Partition of Data into Subsets
6.19Marginalizing in Linear Least Squares
6.20Relative Information of Two Gaussians
6.21Convolution of Two Gaussians
6.22Gradient-Based Optimization Algorithms
6.23Elements of Linear Programming
6.24Spaces and Operators
6.25Usual Functional Spaces
6.26Maximum Entropy Probability Density
6.27Two Properties of ln-Norms
6.28Discrete Derivative Operator
6.29Lagrange Parameters
6.30Matrix Identities
6.31Inverse of a Partitioned Matrix
6.32Norm of the Generalized Gaussian
7 Problems
7.1 Estimation of the Epicentral Coordinates of a Seismic Event
7.2 Measuring the Acceleration of Gravity
7.3 Elementary Approach to Tomography
7.4 Linear Regression with Rounding Errors
7.5 Usual Least-Squares Regression
7.6 Least-Squares Regression with Uncertainties in Both Axes
7.7 Linear Regression with an Outlier
7.8 Condition Number and A Posteriori Uncertainties
7.9 Conjunction of Two Probability Distributions
7.10Adjoint of a Covariance Operator
7.11Problem 7.1 Revisited
7.12Problem 7.3 Revisited
7.13An Example of Partial Derivatives
7.14Shapes of the ln-Norm Misfit Functions
7.15Using the Simplex Method
7.16Problem 7.7 Revisited
7.17Geodetic Adjustment with Outliers
7.18Inversion of Acoustic Waveforms
7.19Using the Backus and Gilbert Method
7.20The Coefficients in the Backus and Gilbert Method
7.21The Norm Associated with the 1D Exponential Covariance
7.22The Norm Associated with the 1D Random Walk
7.23The Norm Associated with the 3D Exponential Covariance
References and References for General Reading
Index
