Description



Table of Contents
Frontmatter -- CONTENTS -- Preface -- Part 1. THEORY AND METHODS OF SOLVING ILL-POSED PROBLEMS -- Generalized maximum likelihood method and its application for solving ill-posed problems -- Iterative method for the solution of nonlinear ill-posed problems and their applications -- Uniform regularization of first kind operator equations in Hilbert space -- On the discretization error in regularized projection methods with parameter choice by discrepancy principle -- Regularization find uniqueness of solutions of systems of Volterra nonlinear integral equations of the first kind with two arguments -- Pointwise residual method for solving systems of linear algebraic equations and inequalities -- Optimality region of the m-step Lavrentiev method -- Multilevel iterative methods for ill-posed problems -- The method of minimal pseudoinversed matrix. Basic statements -- Variational algorithms with a posteriori choice of the regularization parameter for solving ill-posed extremal problems -- Tikhonov's approach for constructing regularizing algorithms -- Regularization algorithms for solving ill-posed criterion problems -- On the numerical solution of the ill-posed problems of construction of approximate solutions of singular integral equations of second kind -- Regularization methods for ill-posed boundary problems -- Modified Tikhonov regularization for nonlinear ill-posed problems leading to optimal convergence rates -- On dynamical restoration of parameters of elliptic systems -- Extreme value estimation, a method for regularizing ill-posed inversion problems -- Two iterative schemes for solving linear non-necessarily well-posed problems in Banach spaces -- On the regularization parameter choice for ill-posed problems with a quasisolution -- An operator method of regularization of nonlinear monotone ill-posed problems -- On the numerical inversion of the Laplace transform with boundary constraints -- Regularization of difference schemes -- Ill-posed problems of on-line conditionally optimal filtering -- The estimation of the error of the regularization method for ill-posed problems with noninjective operator -- Some numerical methods of parameter identification in nonlinear models -- Identification of filtration coefficient -- Ill-posed problems and iterative approximation of fixed points of pseudo-contractive mappings -- Part 2. INVERSE PROBLEMS IN MATHEMATICAL PHYSICS -- Nonlinear inverse problems of acoustic potential -- A measure thoretic approach for studying inverse problems of the heat equation and the wave equation -- New methods and results in multidimensional inverse problems for kinetic equations -- An inverse problem originating from magnetohydrodynamics. Some numerical experiments -- Inverse conductivity problem in the two-dimensional case -- Inverse problems for a system of nonlinear partial differential equations -- An inverse problem in three-dimensional linear thermoviscoelasticity of Boltzmann type -- An inverse boundary value problem for the equation of the plate in the Love-Kirchhoff theory -- Inverse problems for the nonstationary kinetic transport equation -- Optimization methods of solving inverse problems of geoelectrics -- On passage to the limit in the inverse problems for nondivergence parabolic equations -- One method of solution of the inverse problems for layered media -- Identification problems for integrodifferential equations -- The Fredholm solvability of inverse problems for abstract differential equations -- Regularized traces of singular differential operators of higher orders -- Inverse problems for evolution equations -- Inverse problems in mathematical physics -- Stability estimates for inverse problems of geoelectrics -- Inverse problems for elliptic differential operators -- Inverse boundary value problems in viscous fluid dynamics -- On some inverse problems for the time-dependent transport equation -- Determination of constant parameters in some semilinear parabolic equations -- Part 3. A

Ill-Posed Problems in Natural Sciences: Proceedings of the International Conference Held in Moscow, August 19–25, 1991

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    A Hardback by Andrei N. Tikhonov

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      Publisher: De Gruyter
      Publication Date: Publication Date: 31/12/1992
      ISBN13: 9783112302668, 978-3112302668
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      Table of Contents
      Frontmatter -- CONTENTS -- Preface -- Part 1. THEORY AND METHODS OF SOLVING ILL-POSED PROBLEMS -- Generalized maximum likelihood method and its application for solving ill-posed problems -- Iterative method for the solution of nonlinear ill-posed problems and their applications -- Uniform regularization of first kind operator equations in Hilbert space -- On the discretization error in regularized projection methods with parameter choice by discrepancy principle -- Regularization find uniqueness of solutions of systems of Volterra nonlinear integral equations of the first kind with two arguments -- Pointwise residual method for solving systems of linear algebraic equations and inequalities -- Optimality region of the m-step Lavrentiev method -- Multilevel iterative methods for ill-posed problems -- The method of minimal pseudoinversed matrix. Basic statements -- Variational algorithms with a posteriori choice of the regularization parameter for solving ill-posed extremal problems -- Tikhonov's approach for constructing regularizing algorithms -- Regularization algorithms for solving ill-posed criterion problems -- On the numerical solution of the ill-posed problems of construction of approximate solutions of singular integral equations of second kind -- Regularization methods for ill-posed boundary problems -- Modified Tikhonov regularization for nonlinear ill-posed problems leading to optimal convergence rates -- On dynamical restoration of parameters of elliptic systems -- Extreme value estimation, a method for regularizing ill-posed inversion problems -- Two iterative schemes for solving linear non-necessarily well-posed problems in Banach spaces -- On the regularization parameter choice for ill-posed problems with a quasisolution -- An operator method of regularization of nonlinear monotone ill-posed problems -- On the numerical inversion of the Laplace transform with boundary constraints -- Regularization of difference schemes -- Ill-posed problems of on-line conditionally optimal filtering -- The estimation of the error of the regularization method for ill-posed problems with noninjective operator -- Some numerical methods of parameter identification in nonlinear models -- Identification of filtration coefficient -- Ill-posed problems and iterative approximation of fixed points of pseudo-contractive mappings -- Part 2. INVERSE PROBLEMS IN MATHEMATICAL PHYSICS -- Nonlinear inverse problems of acoustic potential -- A measure thoretic approach for studying inverse problems of the heat equation and the wave equation -- New methods and results in multidimensional inverse problems for kinetic equations -- An inverse problem originating from magnetohydrodynamics. Some numerical experiments -- Inverse conductivity problem in the two-dimensional case -- Inverse problems for a system of nonlinear partial differential equations -- An inverse problem in three-dimensional linear thermoviscoelasticity of Boltzmann type -- An inverse boundary value problem for the equation of the plate in the Love-Kirchhoff theory -- Inverse problems for the nonstationary kinetic transport equation -- Optimization methods of solving inverse problems of geoelectrics -- On passage to the limit in the inverse problems for nondivergence parabolic equations -- One method of solution of the inverse problems for layered media -- Identification problems for integrodifferential equations -- The Fredholm solvability of inverse problems for abstract differential equations -- Regularized traces of singular differential operators of higher orders -- Inverse problems for evolution equations -- Inverse problems in mathematical physics -- Stability estimates for inverse problems of geoelectrics -- Inverse problems for elliptic differential operators -- Inverse boundary value problems in viscous fluid dynamics -- On some inverse problems for the time-dependent transport equation -- Determination of constant parameters in some semilinear parabolic equations -- Part 3. A

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