Inverse and Ill-Posed Problems
Published on 10. May 2014
580 pages
978-1-4832-7265-8 (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.
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Heinz W. Engl | C. W. Groetsch
Inverse and Ill-Posed Problems
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09/1987
Academic Press
€70.55
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Content
ContributorsPrefaceA Few Geometrical Features of Inverse and Ill-Posed ProblemsThe Inverse Problem of Aquifer Transmissivity IdentificationReliability of Information Obtained from Approximately-Solved ProblemsThree Topics in Ill-Posed ProblemsA New Approach to Classification and Regularization of Ill-Posed Operator EquationsOn the Optimality of Regularization MethodsOptimal Parameter Choice for Ordinary and Iterated Tikhonov RegularizationParameter Choice for Tikhonov Regularization of Ill-Posed ProblemsFredholm Integral Equations of First Kind and the Method of CorrelogramOn Ill-Posed Problems and the Method of Conjugate GradientsConvergence of the Conjugate Gradient Method for Compact OperatorsComparison Principles for Iterative MethodsComputation of Rough Solutions of Abel Integral EquationsIterative Methods for the Approximate Solution of Ill-Posed Problems with A Priori Information and Their ApplicationsAn Overview of Numerical Methods for Nonlinear Ill-Posed ProblemsSeverely Ill-Posed Radon ProblemsProjection Theorems for Far Field Patterns and the Inverse Scattering ProblemA Numerical Method for an Inverse Scattering ProblemApplied Inverse Problems in OpticsSome Remarks on Locating Radiation SourcesOn the Approximate Solution of a Two-Dimensional Inverse Heat Conduction ProblemModified Equations for Approximating the Solution of a Cauchy Problem for the Heat EquationStability Estimates for Ill-Posed Cauchy Problems for Parabolic EquationsA Boundary Element Collocation Method for the Neumann Problem of the Heat EquationSufficient Conditions for the Solution of the Inverse Vibrating Beam ProblemOn Stabilizing Ill-Posed Problems Against Errors in Geometry and ModelingOn an Ill-Posed Problem for Constant Alpha Force-Free FieldsSome Inverse and Ill-Posed Problems in Computational Fluid DynamicsImproved Continuous Dependence Results for a Class of Evolutionary EquationsSome Boundary Value Problems for the Wave EquationOn the Low Frequency Asymptotics of the Exterior 2-D Dirichlet Problem in Dynamic ElasticityInverse and Ill-Posed Problems in Reservoir SimulationRate of Convergence for the Estimation of a Coefficient in a Two Point Boundary Value ProblemIdentifiability of Distributed ParametersOn the Regularization of Linear Differential-Algebraic EquationsLimits of Abstract SplinesList of Participants
