Inverse and Ill-Posed Problems
Published on 2. September 1987
Book
Hardback
580 pages
978-0-12-239040-1 (ISBN)
Description
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.
More details
Language
English
Place of publication
San Diego
United States
Publishing group
Elsevier Science Publishing Co Inc
Target group
College/higher education
Professional and scholarly
Weight
930 gr
ISBN-13
978-0-12-239040-1 (9780122390401)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Heinz W. Engl | C. W. Groetsch
Inverse and Ill-Posed Problems
E-Book
05/2014
Academic Press
€70.95
Available for download
Content
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
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