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Author:   H.T. Banks ,  K. Kunisch
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   1989 ed.
Weight:   0.605kg
ISBN:  

9780817634339

ISBN 10:   0817634339
Pages:   316
Publication Date:   01 January 1989
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of Contents

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.

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