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

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Andrej N. Tichonov
VSP, 1992 - Science - 594 pages
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The first international conference ''Ill-Posed Problems in Natural Sciences'' was held in Moscow, August 1991. This Proceedings volume contains selected papers by well-known specialists in the theory and applications of ill-posed and inverse problems.
The book covers a wide spectrum of topics such as theoretical mathematical physics, numerical methods in medicine, astrophysics, geophysics, electrodynamics, tomography, mass and heat transport theory, optics and other fields.
 

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Contents

Iterative method for the solution of nonlinear illposed
13
Regularization and uniqueness of solutions of systems
29
Optimality region of the mstep Lavrentiev method
44
The method of minimal pseudoinversed matrix Basic statements
57
Tikhonovs approach for constructing regularizing algorithms
71
Regularization algorithms for solving illposed
84
Modified Tikhonov regularization for nonlinear illposed
104
Extreme value estimation a method for regularizing
118
An inverse boundary value problem for the equation of the plate
300
On passage to the limit in the inverse problems
326
One method of solution of the inverse
333
The Fredholm solvability of inverse problems
367
Inverse problems in mathematical physics
390
Stability estimates for inverse problems of geoelectrics
408
Inverse boundary value problems in viscous fluid dynamics
423
Determination of constant parameters in some semilinear
439

Two iterative schemes for solving linear nonnecessarily
134
An operator method of regularization of nonlinear monotone
149
Regularization of difference schemes
166
The estimation of the error of the regularization
184
Some numerical methods of parameter identification
191
Illposed problems and iterative approximation of fixed points
214
Nonlinear inverse problems of acoustic potential
227
New methods and results in multidimensional inverse problems
244
Inverse conductivity problem in the twodimensional case
270
An inverse problem in threedimensional linear thermoviscoelasticity
284
On numerical methods of solving inverse
454
Inverse problems of astrophysics
472
Methods of solving the ion exchange inverse problem
482
Inverse scattering and synthesis problems
504
A unified approach to the creation of knowledge
525
Inverse problems in electroencephalography and their
543
Regularization method in nonstationary inverse scattering problem
563
On the hypersingular first kind integral equations
584
List of Contributors
595
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