《套用反問題中的計算方法》是2012年高等教育出版社出版的圖書，作者是王彥飛、Anatoly G. Yagola、楊長春。
基本介紹
- 書名：套用反問題中的計算方法
- 作者：王彥飛、Anatoly G. Yagola、楊長春
- ISBN：9787040344998
- 頁數：530
- 定價：139.00元
- 出版社：高等教育出版社
- 出版時間：2012-10
內容簡介,目錄,
內容簡介
《套用反問題中的計算方法(英文版)》主要闡明了環境倫理學的基本理論及其在中國的發展，西方環境倫理學派的發展簡況，環境道德與環境教育的關係，可持續發展和環境立法中的環境倫理，環境倫理的實踐（實踐部分主要包括環境倫理與管理政策、人口、科學技術等）、環境意識中的平等觀等方面的內容。本著簡明扼要的宗旨，《套用反問題中的計算方法(英文版)》重點闡述環境倫理學的基本知識和基本理論。
目錄
Preface
Editor's Preface
Introduction
S. I. Kabanikhin
Inverse Problems of Mathematical Physics
1.1 Introduction
1.2 Examples of Inverse and Ill-posed Problems
1.3 Well-posed and Ill-posed Problems
1.4 The Tikhonov Theorem
1.5 The Ivanov Theorem： Quasi-solution
1.6 The Lavrentiev's Method
1.7 The Tikhonov Regularization Method
References
II Recent Advances in Regularization Theory and Methods
2 D. V. Lukyanenko and A. G. Yagola
Using Parallel Computing for Solving Multidimensional
Ill-posed Problems
2.1 Introduction
2.2 Using Parallel Computing
2.2.1 Main idea of parallel computing
2.2.2 Parallel computing limitations
2.3 Parallelization of Multidimensional Ill-posed Problem
2.3.1 Formulation of the problem and method of solution
2.3.2 Finite-difference approximation of the functional and its gradient
2.3.3 Parallelization of the minimization problem
2.4 Some Examples of Calculations
2.5 Conclusions
References
3 M. T. Nair
Regularization of Fredholm Integral Equations of the First
Kind using Nystrom Approximation
3.1 Introduction
3.2 NystrSm Method for Regularized Equations
3.2.1 NystrSm approximation of integral operators
3.2.2 Approximation of regularized equation
3.2.3 Solvability of approximate regularized equation
3.2.4 Method of numerical solution
3.3 Error Estimates
3.3.1 Some preparatory results
3.3.2 Error estimate with respect to
3.3.3 Error estimate with respect to
3.3.4 A modified method
3.4 Conclusion
References
4 T. Y. Xiao， H. Zhang and L. L. Hao
Regularization of Numerical Differentiation： Methods and
Applications
4.1 Introduction
4.2 Regularizing Schemes
4.2.1 Basic settings
4.2.2 Regularized difference method （RDM）
4.2.3 Smoother-Based regularization （SBR）
4.2.4 Mollifier regularization method （MRM）
4.2.5 Tikhonov's variational regularization （TiVR）
4.2.6 Lavrentiev regularization method （LRM）
4.2.7 Discrete regularization method （DRM）
4.2.8 Semi-Discrete Tikhonov regularization （SDTR）
4.2.9 Total variation regularization （TVR）
4.3 Numerical Comparisons
4.4 Applied Examples
4.4.1 Simple applied problems
4.4.2 The inverse heat conduct problems （IHCP）
4.4.3 The parameter estimation in new product diffusion model
4.4.4 Parameter identification of sturm-liouville operator
4.4.5 The numerical inversion of Abel transform
4.4.6 The linear viscoelastic stress analysis
4.5 Discussion and Conclusion
References
……
Editor's Preface
Introduction
S. I. Kabanikhin
Inverse Problems of Mathematical Physics
1.1 Introduction
1.2 Examples of Inverse and Ill-posed Problems
1.3 Well-posed and Ill-posed Problems
1.4 The Tikhonov Theorem
1.5 The Ivanov Theorem： Quasi-solution
1.6 The Lavrentiev's Method
1.7 The Tikhonov Regularization Method
References
II Recent Advances in Regularization Theory and Methods
2 D. V. Lukyanenko and A. G. Yagola
Using Parallel Computing for Solving Multidimensional
Ill-posed Problems
2.1 Introduction
2.2 Using Parallel Computing
2.2.1 Main idea of parallel computing
2.2.2 Parallel computing limitations
2.3 Parallelization of Multidimensional Ill-posed Problem
2.3.1 Formulation of the problem and method of solution
2.3.2 Finite-difference approximation of the functional and its gradient
2.3.3 Parallelization of the minimization problem
2.4 Some Examples of Calculations
2.5 Conclusions
References
3 M. T. Nair
Regularization of Fredholm Integral Equations of the First
Kind using Nystrom Approximation
3.1 Introduction
3.2 NystrSm Method for Regularized Equations
3.2.1 NystrSm approximation of integral operators
3.2.2 Approximation of regularized equation
3.2.3 Solvability of approximate regularized equation
3.2.4 Method of numerical solution
3.3 Error Estimates
3.3.1 Some preparatory results
3.3.2 Error estimate with respect to
3.3.3 Error estimate with respect to
3.3.4 A modified method
3.4 Conclusion
References
4 T. Y. Xiao， H. Zhang and L. L. Hao
Regularization of Numerical Differentiation： Methods and
Applications
4.1 Introduction
4.2 Regularizing Schemes
4.2.1 Basic settings
4.2.2 Regularized difference method （RDM）
4.2.3 Smoother-Based regularization （SBR）
4.2.4 Mollifier regularization method （MRM）
4.2.5 Tikhonov's variational regularization （TiVR）
4.2.6 Lavrentiev regularization method （LRM）
4.2.7 Discrete regularization method （DRM）
4.2.8 Semi-Discrete Tikhonov regularization （SDTR）
4.2.9 Total variation regularization （TVR）
4.3 Numerical Comparisons
4.4 Applied Examples
4.4.1 Simple applied problems
4.4.2 The inverse heat conduct problems （IHCP）
4.4.3 The parameter estimation in new product diffusion model
4.4.4 Parameter identification of sturm-liouville operator
4.4.5 The numerical inversion of Abel transform
4.4.6 The linear viscoelastic stress analysis
4.5 Discussion and Conclusion
References
……
