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

### Common terms and phrases

Akad algorithm applications approximate solution Arsenin assume assumptions Banach space boundary value problem bounded calculation Cauchy problem coefficients consider constant convergence corresponding defined denote determine difference schemes differential equations direct problem Dirichlet problem Dokl domain element error estimate exists finite formulation given Goncharskii Hilbert space identification problem ill-posed problems inequality integral equation inverse problem inverse scattering problem iterative methods layers LEMMA Leonov linear operator Math mathematical matrix methods for solving minimal Morozov Moscow in Russian Moscow State University Nauk Nauka nonlinear nonstationary norm Novosibirsk numerical methods obtain operator equation optimal Orlovskii parabolic equation parameter choice Prilepko priori properties pseudoinversed Publ reconstruction regularization parameter respect Russia ABSTRACT satisfying sequence solution of problem solvable solving ill-posed stability surface THEOREM theory Tikhonov regularization tion TVP Sci unique solution unknown Vainikko Vasin vector VSP/TVP wave Yagola