英文
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￥ 21.3 7.6折 ￥ 28 全新
库存17件
湖北武汉
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作者（德）佛罗莱恩·弗吕豪夫
出版社哈尔滨工业大学出版社
ISBN9787560398549
出版时间2022-05
装帧平装
开本其他
定价28元
货号9787560398549
上书时间2024-01-23
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目录
1 Introduction
I Regularization Methods
2 Analysis of regularization methods
2.1 Linear regularization
2.2 Nonlinear Tikhonov regularization
2.3 BV functions, sets of finite perimeter and their relation to level sets
2.4 Level set regularization
2.4.1 Analysis of Level Set Regularization
2.4.2 Towards an Analysis of Level Set Regularization Techniques
2.4.3 Minimizing Concept
2.4.4 Convergence Analysis ffinctiohs
2.5 Ginzburg-Landau regularization
2.5.1 Ginzburg-Landan functional
2.5.2 Regularization with a Ginzburg-Landau functional
3 Numerical implementation of regularizatiou methods
3.1 Continuous regularizatinn and a connection to iterative regularization
3.1.1 Continuous regularization
3.1.2 Convex analysis
3.1.3 Connection between continuous and iterative regu]arization
3.2 Implementation of the level set regularization
3.2.1 Numerical solution
3.2.2 Iterative Regularization and the Relation to Dynamic Level Set Methods
3.3 Implementation of the Ginzhurg-Landan regularization method
3.4 Numerical examples
3.4.1 The inverse conductivity problem
3.4.2 Implementation
3.4.3 Results and Discussion
II A parabolic-elliptic problem
4 The direct problem
4.1 Analysis of the parabolic-elliptic problem
4.2 Numerical realization of the parabolic-elliptic problem
4.2.1 Reformulation of the direct problem
4.2.2 Convergence analysis of the reformulated problem
4.2.3 Implementation of the reformulated problem
4.2.4 Numerical examples
5 The inverse problem
5.1 The Factorization Method
5.1.1 The Factorization of A0 - A1
5.1.2 Range characterization
5.1.3 Characterization of the inclusion
5.2 Implementation of the inverse problem
5.2.1 Implementation by regularization
5.2.2 Implementation applying the Picard criterion
5.2.3 Numerical examples
A Additional results:constraint ill-posed operator equation
A.1 A modified level set regularization method
A.2 Ginzburg-Landau Regularization
A.3 Implementation of the constraint operator equation
A.4 Examples of the numerical implementation
B Additional results:Image processing
内容摘要
本书是一部原版引进的英文版应用数学专著。在本书中，作者研究了解决某些反问题的方法，根据Hadamard的观点，如果存在专享的解并且该解持续依赖于数据，那么这个问题就很突出了，如果该解的某一个性质不满足这个问题，那么这种情况叫作不适定的.逆问题通常是不适定的.在许多应用中，可能不需要去详细地解反问题.人们通常只对确定区域感兴趣，这些区域的某些物理性质与参考条件不同.比如，在非破坏性材料测试中，人们总是寻找问题中的孔洞、裂缝或包含物.在包含和周围地区中划分的这种区域被叫作二进制截断.在本著作中作者研究了解决这种二进制反问题的三种不同的方法。
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