Inverse problems

• 作者: Ramm, A. G.
• 出版: New York : Springer Science ©2005.
• 稽核項: 1 online resource (xx, 442 pages).
• 叢書名: Mathematical and analytical techniques with applications to engineering
• 標題: TECHNOLOGY & ENGINEERING Reference. , TECHNOLOGY & ENGINEERING , Reference. , TECHNOLOGY & ENGINEERING Engineering (General) , Electronic books. , Inverse problems (Differential equations) , Ingénierie. , Engineering (General) , Engineering mathematics.
• ISBN: 0387321837 , 9780387321837
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• 附註: Includes bibliographical references (pages 425-439) and index. Cover -- Table of Contents -- Foreword -- Preface -- 1. Introduction -- 1.1 Why are inverse problems interesting and practically important? -- 1.2 Examples of inverse problems -- 1.3 Ill-posed problems -- 1.4 Examples of Ill-posed problems -- 2. Methods of solving ill-posed problems -- 2.1 Variational regularization -- 2.2 Quasisolutions, quasinversion, and Backus-Gilbert method -- 2.3 Iterative methods -- 2.4 Dynamical system method (DSM) -- 2.5 Examples of solutions of ill-posed problems -- 2.6 Projection methods for ill-posed problems -- 3. One-dimensional inverse scattering and spectral problems -- 3.1 Introduction -- 3.2 Property C for ODE -- 3.3 Inverse problem with I-function as the data -- 3.4 Inverse spectral problem -- 3.5 Inverse scattering on half-line -- 3.6 Inverse scattering problem with fixed-energy phase shifts as the data -- 3.7 Inverse scattering with "incomplete data" -- 3.8 Recovery of quarkonium systems -- 3.9 Krein's method in inverse scattering -- 3.10 Inverse problems for the heat and wave equations -- 3.11 Inverse problem for an inhomogeneous Schrèodinger equation -- 3.12 An inverse problem of ocean acoustics -- 3.13 Theory of ground-penetrating radars -- 4. Inverse obstacle scattering -- 4.1 Statement of the problem -- 4.2 Inverse obstacle scattering problems -- 4.3 Stability estimates for the solution to IOSP -- 4.4 High-frequency asymptotics of the scattering amplitude and inverse -- 4.5 Remarks about numerical methods for finding S from the scattering -- 4.6 Analysis of a method for identification of obstacles -- 5. Stability of the solutions to 3D Inverse scattering problems with fixed-energy -- 5.1 Introduction -- 5.2 Inverse potential scattering problem with fixed-energy data -- 5.3 Inverse geophysical scattering with fixed-frequency -- 5.4 Proofs of some estimates -- 5.5 Construction of the Dirichlet-to-Neumann map from the scattering data -- 5.6 Property C -- 5.7 Necessary and sufficient condition for scatterers to be spherica
• 摘要: "Inverse problems are problems that consist of finding an unknown property of an object or medium through the observation of a response from this object or medium to a probing signal. Thus, the theory of inverse problems yields a theoretical basis for remote sensing and non-destructive evaluation. For example, if an acoustic plane wave is scattered by an obstacle, and one observes the scattered field from the obstacle, or in some exterior region, then the inverse problem is to find the shape and material properties of the obstacle. Such problems are important in the identification of flying objects (airplanes, missiles etc.), objects immersed in water (submarines, fish), and in many other situations." "This book presents the theory of inverse spectral and scattering problems and of many other inverse problems for differential equations in an essentially self-contained way. An outline of the theory of ill-posed problems is given because inverse problems are often ill-posed. There are many novel features in this book. The concept of property C, introduced by the author, is developed and used as the basic tool for a study of a wide variety of one- and multi-dimensional inverse problems, making the theory easier and shorter."--Jacket.
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• 系統號: 005315267
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