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Direct methods of solving multidimensional inverse hyperbolic problems /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Utrecht ; Boston, MA :
VSP,
2005.
|
| Colección: | Inverse and ill-posed problems series ;
v. 48. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Intro; Main definitions and notations; Introduction; Chapter 1. Finite-difference scheme inversion (FDSI); 1.1. Introduction; 1.2. Volterra operator equations; 1.3. Definitions and examples; 1.4. Convergence of FDSI; 1.5. Numerical examples; Chapter 2. Linearized multidimensional inverse problem for the wave equation; 2.1. Introduction; 2.2. Problem formulation; 2.3. Linearization; 2.4. Analyzing the structure of the solution to one-dimensional direct problem; 2.5. Existence theorem for the direct problem; 2.6. Uniqueness of solutions to the inverse problem and regularization.
- 2.7. Numerical examplesChapter 3. Methods of I.M. GePfand, B.M. Levitan and M.G. Krein; 3.1. Introduction; 3.2. Gel'fand-Levitan-Krein (GLK) equation for one-dimensional inverse problem; 3.3. Multidimensional analog of GLK-equations; 3.4. Gel'fand-Levitan method for wave equation; 3.5. Discrete analog of the Gel'fand-Levitan equation; 3.6. Multidimensional discrete analog; 3.7. Numerical examples; Chapter 4. Boundary control method (BC method); 4.1. Introduction. Statement of the problem; 4.2. BC method in one-dimensional case; 4.3. BC method for 2D acoustic inverse problem.
- 4.4. Numerical examplesChapter 5. Projection method; 5.1. Introduction; 5.2. Projection method for solving inverse problem for the wave equation; 5.3. Projection method for solving inverse acoustic problem; 5.4. Numerical examples; Appendix A; Appendix B; Bibliography.