Author | Banks, H. T. author |
---|---|
Title | Estimation Techniques for Distributed Parameter Systems [electronic resource] / by H. T. Banks, K. Kunisch |
Imprint | Boston, MA : Birkhรคuser Boston, 1989 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-3700-6 |
Descript | XIV, 316 p. online resource |
I Examples of Inverse Problems Arising in Applications -- I.1. Inverse Problems in Ecology -- I.2. Inverse Problems in Lake and Sea Sedimentation Analysis -- I.3. Inverse Problems in the Study of Flexible Structures -- I.4. Inverse Problems in Physiology -- II Operator Theory Preliminaries -- II.1. Linear Semigroups -- II.2. Galerkin Schemes -- III Parameter Estimation: Basic Concepts and Examples -- III.1. The Parameter Estimation Problem -- III.2. Application of the Theory to Special Schemes for Linear Parabolic Systems -- III.3. Parameter Dependent Approximation and the Nonlinear Variation of Constants Formula -- IV Identifiability and Stability -- IV.1. Generalities -- IV.2. Examples -- IV.3. Identifiability and Stability Concepts -- IV.4. A Sufficient Condition for Identifiability -- IV.5. Output Least Squares Identifiability -- IV.6. Output Least Squares Stability -- IV.7. Regularization -- IV.8. Concluding Remarks on Stability -- V Parabolic Equations -- V.1. Modal Approximations: Discrete Fit-to-Data Criteria -- V.2. Quasimodal Approximations -- V.3. Operator Factorization: A = -C*C -- V.4. Operator Factorization: A = A1/2A1/2 -- V.5. Numerical Considerations -- V.6. Numerical Test Examples -- V.7. Examples with Experimental Data -- VI Approximation of Unknown Coefficients in Linear Elliptic Equations -- VI.1. Parameter Estimation Convergence -- VI.2. Function Space Parameter Estimation Convergence -- VI.3. Rate of Convergence for a Special Case -- VI.4. Methods Other Than Output-Least-Squares -- VI.5. Numerical Test Examples -- VII An Annotated Bibliography -- Al) Preliminaries -- A2) Linear Splines -- A3) Cubic Hermite Splines -- A5) Polynomial Splines, Quasi- Interpolation