Cover Image

$J$-fractional regularization of linear ill-posed equations

We present a method for solution of linear ill-posed equations in function spaces based on the use of continuous $J$-fractions. We obtain a meromorphic solution of regularized equations and indicate some cases where a solution can be represented in terms of rational functions.

Saved in:

Bibliographic Details
Date:	1996
Main Authors:	Syavavko, M. S., Сявавко, М. С.
Format:	Article
Language:	Ukrainian
Published:	Institute of Mathematics, NAS of Ukraine 1996
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/5257
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

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

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

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

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

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

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)

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

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

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

Transformation of formal expansions of solutions of linear differential equations in a parameter into continued RITZ-fractions
by: Rozhankovskaya, M. I., et al.
Published: (1998)

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

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

Optimization of projection schemes of digitization of ill-posed problems
by: Solodkii, S. G., et al.
Published: (1999)

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

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

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)

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

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

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

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)

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)

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

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

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

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

Well-Posed and Regular Nonlocal Boundary-Value Problems for Partial Differential Equations
by: Kengne, E.
Published: (2002)

Well-Posed and Regular Nonlocal Boundary-Value Problems for Partial Differential Equations
by: Kengne, E., et al.
Published: (2002)

Algorithm for estimating solutions of ill-conditioned systems linear algebraic equations
by: V. I. Masol, et al.
Published: (2018)

J-дробова регуляризація лінійних некоректних рівнянь
by: Сявавко, М.С.
Published: (1996)

Generalization of the Cramer Formula
by: Syavavko, M. S., et al.
Published: (2001)

Problems, methods and algorithms for solving linear systems with ill-conditioned matrices
by: V. S. Abramchuk, et al.
Published: (2016)

Two-dimensional regular C-fractions
by: Kh. Y. Kuchminska
Published: (2012)

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

Generalized linear isotherm regularity equation of state applied to metals
by: Sun, H., et al.
Published: (2012)

Optimizations Methods for Solving Linear Systems Ax=b with Ill-conditioned Matrices
by: V. S. Abramchuk, et al.
Published: (2017)

Three-dimensional generalization of regular corresponding C-fraction
by: Kh. Y. Kuchminska, et al.
Published: (2021)

Equivalence of two methods for construction of regular continued C-fractions
by: Katsala, R. A., et al.
Published: (2009)