Ill-posed problems in natural sciences : proceedings of international conference held in Moscow, August 19-25, 1991 / edited by Andrei N. Tikhonov ; editors, A.S. Leonov [and four others].

Format:

Book

Contributor:

Tikhonov, A. N. (Andreĭ Nikolaevich), 1906-1993, editor.

Leonov, A. S., editor.

Language:

English

Subjects (All):

Numerical analysis--Improperly posed problems--Congresses.

Numerical analysis.

Physical Description:

1 online resource (XII, 594 p.)

Edition:

Reprint 2020

Place of Publication:

Utrecht, The Netherlands ; Tokyo, Japan ; Moscow, Russia : VSP : TVP, [1992]

Language Note:

In English.

Contents:

Ill-Posed Problems in Natural Sciences

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

Notes:

Description based on print version record.

ISBN:

9783112313930

3112313933

OCLC:

1158159510