Cover Image

Optimization of projection schemes of digitization of ill-posed problems

We construct new projection schemes of digitization of ill-posed problems, which are optimal in the sense of the amount of discrete information used. We establish that the application of self-adjoint projection schemes to digitization of equations with self-adjoint operators is not optimal.

Saved in:

Bibliographic Details
Date:	1999
Main Authors:	Solodkii, S. G., Солодкий, С. Г.
Format:	Article
Language:	Russian English
Published:	Institute of Mathematics, NAS of Ukraine 1999
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/4739
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
Download file:

Institution

Ukrains’kyi Matematychnyi Zhurnal

Similar Items

Complexity of projective methods for the solution of ill-posed problems
by: Solodkii, S. G., et al.
Published: (1996)

Optimal discretization of Ill-posed problems
by: Pereverzev, S. V., et al.
Published: (2000)

On the optimization of projection-iterative methods for the approximate solution of ill-posed problems
by: Pereverzev, S. V., et al.
Published: (1996)

Hyperbolic cross and complexity of various classes of linear ill-posed problems
by: Myleiko, G. L., et al.
Published: (2017)

Improving the accuracy of the solution of ill-posed discrete problem by random projection
by: E. G. Revunova
Published: (2018)

The Technology of the Stable Solution for Discrete Ill-Posed Problems by Modified Random Projection Method
by: E. G. Revunova, et al.
Published: (2022)

Mathematical Model for Description of Ill-Posed Problems
by: Goncharenko, Yu. Yu.
Published: (2014)

Studying the Accuracy for the Solution of Discrete Ill-Posed Problems Using the Method of Random Projection
by: O. H. Revunova
Published: (2018)

On finite-dimensional approximation of solutions of ill-posed problems
by: Urumbaev, A. N., et al.
Published: (1997)

Information complexity of projection algorithms for the solution of Fredholm equations of the first kind. II
by: Solodkii, S. G., et al.
Published: (1998)

Information complexity of projection algorithms for the solution of Fredholm equations of the first kind. I
by: Solodkii, S. G., et al.
Published: (1998)

Regularization methods for ill-posed problems of quantum optics
by: V. M. Starkov
Published: (2022)

On the coordinated approximation method for nonlinear ill-posed problems
by: Pham Ky Anh
Published: (1994)

Stochastic regularization of ill-posed problems of heat transfer
by: V. V. Panin, et al.
Published: (2014)

Coordinated approximation method for nonlinear ill-posed problems
by: Pham, Ky Anh., et al.
Published: (1994)

On the efficient method of solving ill-posed problems by adaptive discretization
by: Solodky, S.G., et al.
Published: (2009)

Optimization of algorithms for the approximate solution of the Volterra equations with infinitely differentiable kernels
by: Solodkii, S. G., et al.
Published: (1994)

Regularization of One Conditionally Ill-Posed Problem of Extractive Metallurgy
by: Bolshakov, V.I., et al.
Published: (2018)

$J$-fractional regularization of linear ill-posed equations
by: Syavavko, M. S., et al.
Published: (1996)

Linear model selection criteria for the solution of discrete ill-posed problems on the basis of singular value decomposition and random projection
by: E. G. Revunova
Published: (2016)

Hyperbolic cross and complexity of various classes of linear ill-posed problems
by: H. L. Myleiko, et al.
Published: (2017)

Discrepancy Principle and Convergence Rates in Regularization of Monotone Ill-Posed Problems
by: Nguyen Buong
Published: (2003)

Discrepancy Principle and Convergence Rates in Regularization of Monotone Ill-Posed Problems
by: Nguen, Byong, et al.
Published: (2003)

Projection-iteration implementation of explicit variation type methods of solving ill-posed operator equations
by: L. L. Gart
Published: (2017)

On the conditions of convergence for one class of methods used for the solution of ill-posed problems
by: Lebedeva, E. V., et al.
Published: (2008)

Least-squares method in the theory of ill-posed linear boundary-value problems with pulse action
by: Chuiko, S. M., et al.
Published: (2010)

Complexity of fredholm equations of the second kind with kernels from anisotropic classes of differentiable functions
by: Solodkii, S. G., et al.
Published: (1996)

On information complexity of certain classes of operator equations
by: Solodkii, S. G., et al.
Published: (1997)

Convergence rates and finite-dimensional approximation for a class of ill-posed variational inequalities
by: Nguyen Buong
Published: (1997)

Newton-Kantorovich Iterative Regularization for Nonlinear Ill-Posed Equations Involving Accretive Operators
by: Nguen Byong, et al.
Published: (2005)

Newton-Kantorovich Iterative Regularization for Nonlinear Ill-Posed Equations Involving Accretive Operators
by: Vu, Quang Hung, et al.
Published: (2005)

Convergence rates and finite-dimensional approximation for a class of ill-posed variational inequalities
by: Nguen, Byong, et al.
Published: (1997)

On one approach to the discretization of the lavrent’ev method
by: Pereverzev, S. V., et al.
Published: (1996)

On direct methods for solution of regularized equations
by: Pereverzev, S. V., et al.
Published: (1995)

Asymptotically Well-Posed Boundary-Value Problems
by: Kengne, E., et al.
Published: (2004)

On optimization of numerical differentiation methods for bivariate functions
by: Solodky , S. G., et al.
Published: (2022)

Mixed problem for the Petrovskii well-posed equation in a cylindrical domain
by: Iskenderov, B. A., et al.
Published: (2009)

Оптимизация проекционных схем дискретизации некорректных задач
by: Солодкий, С.Г.
Published: (1999)

Оптимизация адаптивных прямых методов решения операторных уравнений в гильбертовом пространстве
by: Солодкий, С.Г.
Published: (1990)

Сложность уравнений Фредгольма II рода с ядрами из анизотропных классов дифференцируемых функций
by: Солодкий, С.Г.
Published: (1996)