Global convergence for ill-posed equations with monotone operators: the dynamical systems method
动力系统
2016-09-07 v1
摘要
Consider an operator equation in a real Hilbert space. Let us call this equation ill-posed if the operator is not boundedly invertible, and well-posed otherwise. If is monotone operator, then we construct a Cauchy problem, which has the following properties: 1) it has a global solution for an arbitrary initial data, 2) this solution tends to a limit as time tends to infinity, 3) the limit is the minimum norm solution to the equation . Example of applications to linear ill-posed operator equation is given.
引用
@article{arxiv.math/0409325,
title = {Global convergence for ill-posed equations with monotone operators: the dynamical systems method},
author = {A. G. Ramm},
journal= {arXiv preprint arXiv:math/0409325},
year = {2016}
}