Inverse and Ill-Posed Problems

Inverse and Ill-Posed Problems

1st Edition - September 2, 1987

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  • Editors: Heinz W. Engl, C. W. Groetsch
  • eBook ISBN: 9781483272658

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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.

Table of Contents


  • 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

Product details

  • No. of pages: 580
  • Language: English
  • Copyright: © Academic Press 1987
  • Published: September 2, 1987
  • Imprint: Academic Press
  • eBook ISBN: 9781483272658

About the Editors

Heinz W. Engl

C. W. Groetsch

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