模型参数估计的反问题理论与方法

所属分类:数学  
出版时间:2009-1   出版时间:科学出版社   作者:塔兰托拉   页数:342  
Tag标签:反演,统计学  

前言

  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。

内容概要

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. ...

书籍目录

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

图书封面

图书标签Tags

反演,统计学


    模型参数估计的反问题理论与方法下载



用户评论 (总计26条)

 
 

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