模型参数估计的反问题理论与方法
2009-1
科学出版社
塔兰托拉
342
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要使我国的数学事业更好地发展起来，需要数学家淡泊名利并付出更艰苦地努力。另一方面，我们也要从客观上为数学家创造更有利的发展数学事业的外部环境，这主要是加强对数学事业的支持与投资力度，使数学家有较好的工作与生活条件，其中也包括改善与加强数学的出版工作。 从出版方面来讲，除了较好较快地出版我们自己的成果外，引进国外的先进出版物无疑也是十分重要与必不可少的。从数学来说，施普林格（springer）出版社至今仍然是世界上最具权威的出版社。科学出版社影印一批他们出版的好的新书，使我国广大数学家能以较低的价格购买，特别是在边远地区工作的数学家能普遍见到这些书，无疑是对推动我国数学的科研与教学十分有益的事。 这次科学出版社购买了版权，一次影印了23本施普林格出版社出版的数学书，就是一件好事，也是值得继续做下去的事情。大体上分一下，这23本书中，包括基础数学书5本，应用数学书6本与计算数学书12本，其中有些书也具有交叉性质。这些书都是很新的，2000年以后出版的占绝大部分，共计16本，其余的也是1990年以后出版的。这些书可以使读者较快地了解数学某方面的前沿，例如基础数学中的数论、代数与拓扑三本，都是由该领域大数学家编著的“数学百科全书”的分册。对从事这方面研究的数学家了解该领域的前沿与全貌很有帮助。按照学科的特点，基础数学类的书以“经典”为主，应用和计算数学类的书以“前沿”为主。这些书的作者多数是国际知名的大数学家，例如《拓扑学》一书的作者诺维科夫是俄罗斯科学院的院士，曾获“菲尔兹奖”和“沃尔夫数学奖”。这些大数学家的著作无疑将会对我国的科研人员起到非常好的指导作用。 当然，23本书只能涵盖数学的一部分，所以，这项工作还应该继续做下去。更进一步，有些读者面较广的好书还应该翻译成中文出版，使之有更大的读者群。 总之，我对科学出版社影印施普林格出版社的部分数学著作这一举措表示热烈的支持，并盼望这一工作取得更大的成绩。
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. ...
Preface1 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 Problem2 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 Annealing3 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 Hessian4 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 Problems5 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 Waveforms6 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 6.10 Sequential Random Realization 6.11 Cascaded Metropolis Algorithm 6.12 Distance and Norm 6.13 The Different Meanings of the Word Kernel 6.14 Transpose and Adjoint of a Differential Operator 6.15 The Bayesian Viewpoint of Backus (1970) 6.16 The Method of Backus and Gilbert 6.17 Disjunction and Conjunction of Probabilities 6.18 Partition of Data into Subsets 6.19 Marginalizing in Linear Least Squares 6.20 Relative Information of Two Gaussians 6.21 Convolution of Two Gaussians 6.22 Gradient-Based Optimization Algorithms 6.23 Elements of Linear Programming 6.24 Spaces and Operators 6.25 Usual Functional Spaces 6.26 Maximum Entropy Probability Density 6.27 Two Properties of ln-Norms 6.28 Discrete Derivative Operator 6.29 Lagrange Parameters 6.30 Matrix Identities 6.31 Inverse of a Partitioned Matrix 6.32 Norm of the Generalized Gaussian7 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 7.10 Adjoint of a Covariance Operator 7.11 Problem 7.1 Revisited 7.12 Problem 7.3 Revisited 7.13 An Example of Partial Derivatives 7.14 Shapes of the ln-Norm Misfit Functions 7.15 Using the Simplex Method 7.16 Problem 7.7 Revisited 7.17 Geodetic Adjustment with Outliers 7.18 Inversion of Acoustic Waveforms 7.19 Using the Backus and Gilbert Method 7.20 The Coefficients in the Backus and Gilbert Method 7.21 The Norm Associated with the 1D Exponential Covariance 7.22 The Norm Associated with the 1D Random Walk 7.23 The Norm Associated with the 3D Exponential CovarianceReferences and References for General ReadingIndex
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很不错的一本介绍反演理论的书籍。推荐搞反演工作的人阅读。
对于经常遇到反问题的工程技术研究人员来讲，值得一读！
经典名著，书的内容没得说。
这本是补充，还需要前传。
偶像的书
数写的一般