- 逆问题的数学理论导论(第2版)(英文版)
- - 作者：(德)基尔施
  - 出版社：世界图书出版公司
  - ISBN：9787519202675
  - 出版日期：2016/03/01
  - 页数：307
- 售价：22

内容大纲
基尔施著的这本《逆问题的数学理论导论（第2版）（英文版）》将带领读者进入逆问题领域。逆问题的研究对许多科技领域诸如地球物理探测、系统识别、无损检测及超声层析成像等，有着重要的作用。本书分两部分。第一部分讲不适定问题的基本概念和困难。书中通过几个简单的解析数值算例研究了线性不适定问题正则法的基本特征。第二部分详细地研究了三个特殊非线性逆问题，即逆谱问题、电阻抗断层成像逆问题和逆散射问题。
本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。
作者介绍
目录
1 Introduction and Basic Concepts
  1.1 Examples oflnverse Problems
  1.2 Ill-Posed Problems
  1.3 The Worst-Case Error
  1.4 Problems
2 Regularization Theory for Equations of the First Kind
  2.1 A General Regularization Theory
  2.2 Tikhonov Regularization
  2.3 Landweber Iteration
  2.4 A Numerical Example
  2.5 The Discrepancy Principle of Morozov
  2.6 Landweber's Iteration Method with Stopping Rule
  2.7 The Conjugate Gradient Method
  2.8 Problems
3 Regularization by Discretization
  3.1 Projection Methods
  3.2 Galerkin Methods
    3.2.1 The Least Squares Method
    3.2.2 The Dual Least Squares Method
    3.2.3 The Bubnov-Galerkin Method for Coercive Operators
  3.3 Application to Symm's Integral Equation of the First Kind
  3.4 Collocation Methods
    3.4.1 Minimum Norm Collocation
    3.4.2 Collocation of Symm's Equation
  3.5 Numerical Experiments for Symm's Equation
  3.6 The Backus-Gilbert Method
  3.7 Problems
4 Inverse Eigenvalue Problems
  4.1 Introduction
  4.2 Construction of a Fundamental System
  4.3 Asymptotics of the Eigenvalues and Eigenfunctions
  4.4 Some Hyperbolic Problems
  4.5 The Inverse Problem
  4.6 A Parameter Identification Problem
  4.7 Numerical Reconstruction Techniques
  4.8 Problems
5 An Inverse Problemin Electrical Impedance Tomography
  5.1 Introduction
  5.2 The Direct Problem and the Neumann-Dirichlet Operator
  5.3 The Inverse Problem
  5.4 The Factorization Method
  5.5 Problems
6 An Inverse Scattering Problem
  6.1 Introduction
  6.2 The Direct Scattering Problem
  6.3 Properties of the Far Field Patterns
  6.4 Uniqueness of the Inverse Problem
  6.5 The Factorization Method
  6.6 Numerical Methods
    6.6.1 A Simplified Newton Method

    6.6.2 A Modified Gradient Method
    6.6.3 The Dual Space Method
  6.7 Problems
A Basic Facts from Functional Analysis
  A.1 Normed Spaces and Hilbert Spaces
  A.2 Orthonormal Systems
  A.3 Linear Bounded and Compact Operators
  A.4 Sobolev Spaces of Periodic Functions
  A.5 Sobolev Spaces on the Unit Disc
  A.6 Spectral Theory for Compact Operators in Hilbert Spaces
  A.7 The Frechet Derivative
B Proofs of the Results of Section 2.7
References
Index

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作者介绍

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