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Contributors

Preface

A Few Geometrical Features of Inverse and Ill-Posed Problems

The Inverse Problem of Aquifer Transmissivity Identification

Reliability of Information Obtained from Approximately-Solved Problems

Three Topics in Ill-Posed Problems

A New Approach to Classification and Regularization of Ill-Posed Operator Equations

On the Optimality of Regularization Methods

Optimal Parameter Choice for Ordinary and Iterated Tikhonov Regularization

Parameter Choice for Tikhonov Regularization of Ill-Posed Problems

Fredholm Integral Equations of First Kind and the Method of Correlogram

On Ill-Posed Problems and the Method of Conjugate Gradients

Convergence of the Conjugate Gradient Method for Compact Operators

Comparison Principles for Iterative Methods

Computation of Rough Solutions of Abel Integral Equations

Iterative Methods for the Approximate Solution of Ill-Posed Problems with A Priori Information and Their Applications

An Overview of Numerical Methods for Nonlinear Ill-Posed Problems

Severely Ill-Posed Radon Problems

Projection Theorems for Far Field Patterns and the Inverse Scattering Problem

A Numerical Method for an Inverse Scattering Problem

Applied Inverse Problems in Optics

Some Remarks on Locating Radiation Sources

On the Approximate Solution of a Two-Dimensional Inverse Heat Conduction Problem

Modified Equations for Approximating the Solution of a Cauchy Problem for the Heat Equation

Stability Estimates for Ill-Posed Cauchy Problems for Parabolic Equations

A Boundary Element Collocation Method for the Neumann Problem of the Heat Equation

Sufficient Conditions for the Solution of the Inverse Vibrating Beam Problem

On Stabilizing Ill-Posed Problems Against Errors in Geometry and Modeling

On an Ill-Posed Problem for Constant Alpha Force-Free Fields

Some Inverse and Ill-Posed Problems in Computational Fluid Dynamics

Improved Continuous Dependence Results for a Class of Evolutionary Equations

Some Boundary Value Problems for the Wave Equation

On the Low Frequency Asymptotics of the Exterior 2-D Dirichlet Problem in Dynamic Elasticity

Inverse and Ill-Posed Problems in Reservoir Simulation

Rate of Convergence for the Estimation of a Coefficient in a Two Point Boundary Value Problem

Identifiability of Distributed Parameters

On the Regularization of Linear Differential-Algebraic Equations

Limits of Abstract Splines

List of Participants

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1st Edition - September 2, 1987

Editors: Heinz W. Engl, C. W. Groetsch

Language: EnglisheBook ISBN:

9 7 8 - 1 - 4 8 3 2 - 7 2 6 5 - 8

Inverse and Ill-Posed Problems is a collection of papers presented at a seminar of the same title held in Austria in June 1986. The papers discuss inverse problems in various… Read more

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Inverse and Ill-Posed Problems is a collection of papers presented at a seminar of the same title held in Austria in June 1986. The papers discuss inverse problems in various disciplines; mathematical solutions of integral equations of the first kind; general considerations for ill-posed problems; and the various regularization methods for integral and operator equations of the first kind. Other papers deal with applications in tomography, inverse scattering, detection of radiation sources, optics, partial differential equations, and parameter estimation problems. One paper discusses three topics on ill-posed problems, namely, the imposition of specified types of discontinuities on solutions of ill-posed problems, the use of generalized cross validation as a data based termination rule for iterative methods, and also a parameter estimation problem in reservoir modeling. Another paper investigates a statistical method to determine the truncation level in Eigen function expansions and for Fredholm equations of the first kind where the data contains some errors. Another paper examines the use of singular function expansions in the inversion of severely ill-posed problems arising in confocal scanning microscopy, particle sizing, and velocimetry. The collection can benefit many mathematicians, students, and professor of calculus, statistics, and advanced mathematics.

Contributors

Preface

A Few Geometrical Features of Inverse and Ill-Posed Problems

The Inverse Problem of Aquifer Transmissivity Identification

Reliability of Information Obtained from Approximately-Solved Problems

Three Topics in Ill-Posed Problems

A New Approach to Classification and Regularization of Ill-Posed Operator Equations

On the Optimality of Regularization Methods

Optimal Parameter Choice for Ordinary and Iterated Tikhonov Regularization

Parameter Choice for Tikhonov Regularization of Ill-Posed Problems

Fredholm Integral Equations of First Kind and the Method of Correlogram

On Ill-Posed Problems and the Method of Conjugate Gradients

Convergence of the Conjugate Gradient Method for Compact Operators

Comparison Principles for Iterative Methods

Computation of Rough Solutions of Abel Integral Equations

Iterative Methods for the Approximate Solution of Ill-Posed Problems with A Priori Information and Their Applications

An Overview of Numerical Methods for Nonlinear Ill-Posed Problems

Severely Ill-Posed Radon Problems

Projection Theorems for Far Field Patterns and the Inverse Scattering Problem

A Numerical Method for an Inverse Scattering Problem

Applied Inverse Problems in Optics

Some Remarks on Locating Radiation Sources

On the Approximate Solution of a Two-Dimensional Inverse Heat Conduction Problem

Modified Equations for Approximating the Solution of a Cauchy Problem for the Heat Equation

Stability Estimates for Ill-Posed Cauchy Problems for Parabolic Equations

A Boundary Element Collocation Method for the Neumann Problem of the Heat Equation

Sufficient Conditions for the Solution of the Inverse Vibrating Beam Problem

On Stabilizing Ill-Posed Problems Against Errors in Geometry and Modeling

On an Ill-Posed Problem for Constant Alpha Force-Free Fields

Some Inverse and Ill-Posed Problems in Computational Fluid Dynamics

Improved Continuous Dependence Results for a Class of Evolutionary Equations

Some Boundary Value Problems for the Wave Equation

On the Low Frequency Asymptotics of the Exterior 2-D Dirichlet Problem in Dynamic Elasticity

Inverse and Ill-Posed Problems in Reservoir Simulation

Rate of Convergence for the Estimation of a Coefficient in a Two Point Boundary Value Problem

Identifiability of Distributed Parameters

On the Regularization of Linear Differential-Algebraic Equations

Limits of Abstract Splines

List of Participants

- No. of pages: 580
- Language: English
- Edition: 1
- Published: September 2, 1987
- Imprint: Academic Press
- eBook ISBN: 9781483272658

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