Dynamical inverse problems theory and application /
The papers in this volume present an overview of the gerneral aspects and practical applications of dynamic inverse methods, through the interaction of several topics, ranging from classical and advanced inverse problems in vibration, isospectral systems, dynamic methods for structural identificatio...
| Other Authors: | Gladwell, G. M. L., Morassi, Antonino., International Centre for Mechanical Sciences. |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Wien ; New York :
Springer,
©2011.
Wien ; New York : [2011] |
| Physical Description: |
1 online resource (222 pages) : illustrations (some color). |
| Series: |
Courses and lectures ;
no. 529. |
| Subjects: |
Table of Contents:
- Title Page; Copyright Page; PREFACE; Table of Contents; Matrix Inverse Eigenvalue Problems; 1 Lecture 1. Classical Inverse Problems; 1.1 Introduction; 1.2 The Rayleigh Quotient; 1.3 Inverse Problems for a Jacobian Matrix; 2 Lecture 2. Applications and Extensions; 2.1 A Minimal Mass Problem; 2.2 Another Spring-Mass Inverse Problem; 2.3 Inverse Problems for a Pentadiagonal Matrix; 2.4 Periodic Jacobi Matrices; 2.5 Graph Theory; 3 Lecture 3. Isospectral Systems; 3.1 Reversing Factors; 3.2 The QR Algorithm; 3.3 Positivity; 4 Lecture 4. Toda Flow; 4.1 The Basic Equations.
- 4.2 Application of Toda FlowBibliography; An Introduction to Classical Inverse Eigenvalue Problems; 1 Introduction; 2 Properties of the Dirichlet Eigenvalue Problem; 3 Uniqueness Results: the Borg's Approach; 3.1 Symmetric Potential and Dirichlet Boundary Conditions; 3.2 Symmetric Potential and Neumann Boundary Conditions; 3.3 Generic L2 Potential; 4 Uniqueness Towards Stability; 4.1 Hochstadt's Formula; 4.2 A Local Stability Result; 5 A Local Existence Result; 6 An Euler-Bernoulli Inverse Eigenvalue Problem; Bibliography.
- A Least Squares Functional for Solving Inverse Sturm-Liouville Problems1 Inverse Problems with Least Squares; 1.1 Gradient Flow; 2 The Inverse Sturm-Liouville Problem; 2.1 Examples; 3 Recovering boundary conditions; 3.1 Examples; 4 Theory; 4.1 Manifolds; 4.2 From the Wronskian to a Scalar Product; 4.3 Linear Independence of the Eigenfunctions; 4.4 Exponential Convergence; 4.5 Other spectral Data; 4.6 Isospectral Manifolds; 5 Similar Algorithms; Bibliography; Boundary Control Method in Dynamical Inverse Problems
- An Introductory Course; 1 Introduction; 1.1 About the paper.