Ill-Posed Problems in Natural Sciences : : Proceedings of the International Conference Held in Moscow, August 19–25, 1991 / / ed. by Andrei N. Tikhonov.

• Superior document: Title is part of eBook package: De Gruyter DGBA Mathematics - 1990 - 1999
• MitwirkendeR: Alekseyev, G. V.,; Anger, G.,; Anikonov, Yu. E.,; Arsenin, V. Ya.,; Asanov, A. A.,; Bakushinskii, A. B.,; Barashkov, I. S.,; Beretta, E.,; Bersenev, S. M.,; Burov, V. A.,; Chanov, A. V.,; Chebotarev, A. Yu.,; Cherednichenko, V. G.,; Cherepakhin, A. V.,; Cherepashchuk, A. M.,; Denisov, A. M.,; Dmitriev, V. I.,; Dobrowolski, J. A.,; Dubrovskii, V. V.,; Eremin, Ju. A.,; Fedotov, A. M.,; Fischer, E.,; Galkin, V. Ya.,; Goncharskii, A. V.,; Grasselli, M.,; Halejeva, I. V.,; Hämarik, U.,; Ikehata, M.,; Imanaliev, M. I.,; Ivanitskii, A. Yu.,; Ivankov, A. L.,; Kabanikhin, S. I.,; Kamynin, V. L.,; Karchevsky, A. L.,; Karpenko, V. A.,; Kiho, T.,; King, J. T.,; Kochikov, I . V.,; Koptelov, Yu. M.,; Korotkii, A. I.,; Kostin, A. B.,; Krianev, A. V.,; Kuramshina, G. M.,; Lavrent’ev, M. M.,; Leonov, A. S.,; Levin, A. M.,; Lorenzi, A.,; Matveev, A. F.,; Mel’nikova, I. V.,; Morozov, V. A.,; Nagorny, A. V.,; Neubauer, A.,; Nishimura, N.,; Nizhnik, L.,; Onishi, K.,; Orlovskii, D. G.,; Osipov, Yu. S.,; Paatero, P.,; Pechentsov, A. S.,; Pentin, Yu. A.,; Plato, R.,; Prilepko, A. I.,; Raus, T.,; Rjazanceva, I.,; Rodriguez, G.,; Romanenko, R.,; Romanov, V. G.,; Rudakova, T. N.,; Rumiantseva, O. D.,; Sadovnichii, V. A.,; Samarskii, A. A.,; Seatzu, S.,; Sinitsyn, I. N.,; Sveshnikov, A. G.,; Taikina, S. R.,; Tanana, V. P.,; Tikhonov, I. V.,; Vaarmann, O.,; Vabishchevich, P. N.,; Vainikko, G.,; Vasii’ev, F. P.,; Vasin, I. A.,; Vasin, V. V.,; Veryovkina, G. V.,; Vogelius, M.,; Volkov, N. P.,; Yagola, A. G.,; Yamamoto, M.,; Zakharov, E. V.,
• HerausgeberIn: Tikhonov, Andrei N.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2020]; ©1992
• Year of Publication: 2020
• Edition: Reprint 2020
• Language: English
• Physical Description: 1 online resource (XII, 594 p.)

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. APPLICATIONS -- A numerical method for solving inverse problem of deep magnetotelluric quasi-layered media sounding -- On numerical methods of solving inverse problems of electrical prospecting -- The solution stability and restrictions on the space scatterer spectrum in the two-dimensional monochromatic inverse scattering problem -- Inverse problems of astrophysics -- Methods of solving the ion exchange inverse problem in counter-current columns -- Numerical methods for optical thin films at the National Research Council of Canada -- Inverse scattering and synthesis problems in the diffraction theory -- The construction of numerical algorithms for ill-posed problems with random errors in initial data -- A unified approach to the creation of knowledge-based systems for identification of some classes of nonstationary processes -- Inverse problems in vibrational spectroscopy -- Inverse problems in electroencephalography and their numerical solving -- A numerical method of crack determination by the boundary integral equation method -- Regularization method in nonstationary inverse scattering problem -- Numerical methods for inverse scattering problems in two-dimensional scalar field -- On the hypersingular first kind integral equations for problems of electromagnetic scattering from screen surfaces -- List of Contributors -- National Organizing Committee