《计算反演问题中的优化与正则化方法及其应用》是2010年高等教育出版社出版的图书，作者是王彦飞。

• 书名 计算反演问题中的优化与正则化方法及其应用
• 作者 王彦飞
• 出版社 高等教育出版社
• 出版时间 2010年5月1日

图书信息

　　书 名: 计算反演问题中的优化与正则化方法及其应用

　　作 者:王彦飞

　　出版社: 高等教育出版社

　　出版时间: 2010年5月1日

　　ISBN: 9787040285154

　　开本: 16开

　　定价: 79来自.00元

内容简介

　　《计算反演问题中的优化与正则化方法及其应用》内360百科容简介:Optimization and Regularization for Co势随总著规降mputational Inverse Problems and Applications focuses on advances in inversion theory and recent developments with practical applications, particularly emphasi拉zing the combination of optimization and regularization for solving inverse problems. This book cove调便施降善策原洲航rs both the meth呼席现率书ods, including standard regularization theory, Fejer processes fo小绿物文民间请副外该r linear and nonlinear problems, the balan了受步便半露材技国升针cing principle, extrapolated regularization, nonstandard regularization, nonlinear gradient method, the nonmonotone gradient method, subspa皮ce method and 稳已联突立景吸Lie group method; and the practical applications, such as the reconstruction problem for inverse scattering, molecular spectra data processing, quanti跑形燃谈哪tative remote sensing in晶请判各类重耐与做力斯version, seismic inversion using the Lie group method, and the gravitational lensing problem.

　电数达　Scientists, r建铁入烟专任剂种庆丝粒esearchers an气混氢村看导系强督联d engineers, as well as grad未模艺讨失何座映伟程uate students engaged in applied mathematic额烟吗翻血密陈销督责s, engineering, geophysics, medical science, image processing, remote sensing and atmospheric science will benefit from this book.

作者简介

　　编者:王彦飞 (俄国)亚哥拉(Anatoly G.Yagola) 杨长春

　　Dr. Yanfei Wang is a Professor at the Institu八至怀持笑方并静带te of Geology and 压就责理举Geophysics, Chinese Academy of Sciences, China.

　　Dr. Sc来自. Anatoly G. Yagola is a Professor and Assistant Dean of the Physical Faculty, Lomonoso360百科v Moscow State University, Russia.

　　Dr. Changchun Yang is a Professor and Vice Director o原f the Institute of Geology and Geophysics, Chin后势调ese Academy of Sciences, China.

图书目录

　　Part I Introduction

　　1 句席成有候独阶职素对配Inverse Problems, Optimization and Regularization: A Multi-Disciplinary Subject

　　Yanfei Wang and Changchun Yang

　　1.1 Introduction

　　1.2 Examples about mathemat斗自善岩走ical inverse problems

　　1.3 Examples in applied science and engineering

　　1.4 Basic theory

　　1.5 Scientific computing

　　1.6 Conclusion

　　Referertces

　　Part II Regularization Theory and Recent Developmen背协县司属款友呀ts

　　2 Ill-Posed Problems and Methods for Their Numerical Solution

　　An危站命确atoly G. Y合伤持代单景agola

　　2把终致雨思川天粒.1 Well-posed and ill-posed problems

们沿名销都　　2.2 Definition of the regularizing algorithm

　　2.3 Ill-posed problems on compact sets

　　2.4 Ill-pose及区推迫d problems with sourcewise represented solutions

　　2.5 Variational approach for constructing regularizing algorithms

　　2.6 歌杂但创Nonlinea材r ill-posed problems

　　2.7 低肉何Iterative and other methods

　　References

　　3 Inverse Problems with 它A Priori Information

　　Vladimir V. Vasin

　　3.1 Introduction

　　3.2 Formulation of the problem with a priori information

　　3.3 The main classes of mappings of the Fejer type and t官亲运做heir prope提rties

　　3.4 Convergence theorems of the method of successive approximations for the pseudo-contractive operators

　　3.5 Examples of operators of the Fejer type

　　3.6 Fejer processes for nonlinear equations

　　3.7 Applied problems with a priori information and methods for solution

　　3.7.1 Atomic structure characterization

　　3.7.2 Radiolocation of the ionosphere

　　3.7.3 Image reconstruction

　　3.7.4 Thermal sounding of the atmosphere

　　3.7.5 Testing a wellbore/reservoir

　　3.8 Conclusions

　　References

　　4 Regularization of Naturally Linearized Parameter Identification Problems and the Application of the Balancing Principle

　　Hui Cao and Sergei Pereverzyev

　　4.1 Introduction

　　4.2 Discretized Tikhonov regularization and estimation of accuracy

　　4.2.1 Generalized source condition

　　4.2.2 Discretized Tikhonov regularization

　　4.2.3 Operator monotone index functions

　　4.2.4 Estimation of the accuracy

　　4.3 Parameter identification in elliptic equation

　　4.3.1 Natural linearization

　　4.3.2 Data smoothing and noise level analysis

　　4.3.3 Estimation of the accuracy

　　4.3.4 Balancing principle

　　4.3.5 Numerical examples

　　4.4 Parameter identification in parabolic equation

　　4.4.1 Natural linearization for recovering b(x) = a(u(T, x))

　　4.4.2 Regularized identification of the diffusion coefficient a(u)

　　4.4.3 Extended balancing principle

　　4.4.4 Numerical examples

　　References

　　5 Extrapolation Techniques of Tikhonov Regularization

　　Tingyan Xiao, Yuan Zhao and Guozhong Su

　　5.1 Introduction

　　5.2 Notations and preliminaries

　　5.3 Extrapolated regularization based on vector-valued function approximation

　　5.3.1 Extrapolated scheme based on Lagrange interpolation

　　5.3.2 Extrapolated scheme based on Hermitian interpolation

　　5.3.3 Extrapolation scheme based on rational interpolation

　　5.4 Extrapolated regularization based on improvement of regularizing qualification

　　5.5 The choice of parameters in the extrapolated regularizing approximation

　　5.6 Numerical experiments

　　5.7 Conclusion

　　References

　　6 Modified Regularization Scheme with Application in Reconstructing Neumann-Dirichlet Mapping

　　Pingli Xie and Jin Cheng

　　6.1 Introduction

　　6.2 Regularization method

　　6.3 Computational aspect

　　6.4 Numerical simulation results for the modified regularization

　　6.5 The Neumann-Dirichlet mapping for elliptic equation of second order

　　6.6 The numerical results of the Neumann-Dirichlet mapping

　　6.7 Conclusion

　　References

　　Part III Nonstandard Regularization and Advanced Optimization Theory and Methods

　　7 Gradient Methods for Large Scale Convex Quadratic Functions

　　Yaxiang Yuan

　　7.1 Introduction

　　7.2 A generalized convergence result

　　7.3 Short BB steps

　　7.4 Numerical results

　　7.5 Discussion and conclusion

　　References

　　8 Convergence Analysis of Nonlinear Conjugate Gradient Methods

　　Yuhong Dai

　　8.1 Introduction

　　8.2 Some preliminaries

　　8.3 A sufficient and necessary condition on 钣

　　8.3.1 Proposition of the condition

　　8.3.2 Sufficiency of (8.3.5)

　　8.3.3 Necessity of (8.3.5)

　　8.4 Applications of the condition (8.3.5)

　　8.4.1 Property (#)

　　8.4.2 Applications to some known conjugate gradient methods

　　8.4.3 Application to a new conjugate gradient method

　　8.5 Discussion

　　References

　　9 Full Space and Subspace Methods for Large Scale Image Restoration

　　Yanfei Wang, Shiqian Ma and Qinghua Ma

　　9.1 Introduction

　　9.2 Image restoration without regularization

　　9.3 Image restoration with regularization

　　9.4 Optimization methods for solving the smoothing regularized functional

　　9.4.1 Minimization of the convex quadratic programming problem with projection

　　9.4.2 Limited memory BFGS method with projection

　　9.4.3 Subspace trust region methods

　　9.5 Matrix-Vector Multiplication (MVM)

　　9.5.1 MVM: FFT-based method

　　9.5.2 MVM with sparse matrix

　　9.6 Numerical experiments

　　9.7 Conclusions

　　References

　　Part IV Numerical Inversion in Geoscience and Quantitative Remote Sensing

　　10 Some Reconstruction Methods for Inverse Scattering Problems

　　Jijun Liu and Haibing Wang

　　10.1 Introduction

　　10.2 Iterative methods and decomposition methods

　　10.2.1 Iterative methods

　　10.2.2 Decomposition methods

　　10.2.3 Hybrid method

　　10.3 Singular source methods

　　10.3.1 Probe method

　　10.3.2 Singular sources method

　　10.3.3 Linear sampling method

　　10.3.4 Factorization method

　　10.3.5 Range test method

　　10.3.6 No response test method

　　10.4 Numerical schemes

　　References

　　11 Inverse Problems of Molecular Spectra Data Processing

　　Gulnara Kuramshina

　　11.1 Introduction

　　11.2 Inverse vibrational problem

　　11.3 The mathematical formulation of the inverse vibrational problem

　　11.4 Regularizing algorithms for solving the inverse vibrational problem

　　11.5 Model of scaled molecular force field

　　11.6 General inverse problem of structural chemistry

　　11.7 Intermolecular potential

　　11.8 Examples of calculations

　　11.8.1 Calculation of methane intermolecular potential

　　11.8.2 Prediction of vibrational spectrum of fullerene C240

　　References

　　12 Numerical Inversion Methods in Geoscience and Quantitative

　　Remote Sensing

　　Yanfei Wang and Xiaowen Li

　　12.1 Introduction

　　12.2 Examples of quantitative remote sensing inverse problems: land surface parameter retrieval problem

　　12.3 Formulation of the forward and inverse problem

　　12.4 What causes ill-posedness

　　12.5 Tikhonov variational regularization

　　12.5.1 Choices of the scale operator D

　　12.5.2 Regularization parameter selection methods

　　12.6 Solution methods

　　12.6.1 Gradient-type methods

　　12.6.2 Newton-type methods

　　12.7 Numerical examples

　　12.8 Conclusions

　　References

　　13 Pseudo-Differential Operator and Inverse Scattering of Multidimensional Wave Equation

　　Hong Liu, Li He

　　13.1 Introduction

　　13.2 Notations of operators and symbols

　　13.3 Description in symbol domain

　　13.4 Lie algebra integral expressions

　　13.5 Wave equation on the ray coordinates

　　13.6 Symbol expression of one-way wave operator equations

　　13.7 Lie algebra expression of travel time

　　13.8 Lie algebra integral expression of prediction operator

　　13.9 Spectral factorization expressions of reflection data

　　13.10 Conclusions

　　References

　　14 Tikhonov Regularization for Gravitational Lensing Research.

　　Boris Artamonov, Ekaterina Koptelova, Elena Shimanovskaya and Anatoly G. Yagola

　　14.1 Introduction

　　14.2 Regularized deconvolution of images with point sources and smooth background

　　14.2.1 Formulation of the problem

　　14.2.2 Tikhonov regularization approach

　　14.2.3 A priori information

　　14.3 Application of the Tikhonov regularization approach to quasar profile reconstruction

　　14.3.1 Brief introduction to microlensing

　　14.3.2 Formulation of the problem

　　14.3.3 Implementation of the Tikhonov regularization approach

　　14.3.4 Numerical results of the Q2237 profile reconstruction

　　14.4 Conclusions

　　References

　　Index