Ill-Posed and Linear Inverse Problems

author

  • A. Azizi Department of Mathematics, Payame Noor University, PO Box 19395-3697 Tehran, I. R. of Iran.
Abstract:

In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Learning, Regularization and Ill-Posed Inverse Problems

Many works have shown that strong connections relate learning from examples to regularization techniques for ill-posed inverse problems. Nevertheless by now there was no formal evidence neither that learning from examples could be seen as an inverse problem nor that theoretical results in learning theory could be independently derived using tools from regularization theory. In this paper we pro...

full text

Ill - posed inverse problems in economics

A parameter of an econometric model is identified if there is a one-to-one or many-to-one mapping from the population distribution of the available data to the parameter. Often, this mapping is obtained by inverting a mapping from the parameter to the population distribution. If the inverse mapping is discontinuous, then estimation of the parameter usually presents an illposed inverse problem. ...

full text

Hybrid Samplers for Ill-Posed Inverse Problems

In the Bayesian approach to ill-posed inverse problems, regularization is imposed by specifying a prior distribution on the parameters of interest and Markov chain Monte Carlo samplers are used to extract information about its posterior distribution. The aim of this paper is to investigate the convergence properties of the random-scan random-walk Metropolis (RSM) algorithm for posterior distrib...

full text

Linear ill - posed problems and dynamical systems ∗ †

A new approach to solving linear ill-posed problems is proposed. The approach consists of solving a Cauchy problem for a linear operator equation and proving that this problem has a global solution whose limit at infinity solves the original linear equation.

full text

FGMRES for linear discrete ill-posed problems

GMRES is one of the most popular iterative methods for the solution of large linear systems of equations. However, GMRES generally does not perform well when applied to the solution of linear systems of equations that arise from the discretization of linear ill-posed problems with error-contaminated data represented by the right-hand side. Such linear systems are commonly referred to as linear ...

full text

International Conference «Inverse and Ill-Posed Problems of Mathematical Physics»,

Inversion of ill-posed problem from measurement data have been proposed use: i) Conjugate gradient projection method with regularization; ii) Conditional gradient method with regularization; iii) SVD with constraints with regularization method and iv) The method for solving two-dimensional integral equation of convolution type for vector functions using DFT method for Tikhonov functional. The p...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 4  issue 1

pages  131- 138

publication date 2015-06-30

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023