𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Dynamical systems method for ill-posed equations with monotone operators

✍ Scribed by A.G. Ramm

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
283 KB
Volume
10
Category
Article
ISSN
1007-5704

No coin nor oath required. For personal study only.

✦ Synopsis

Consider an operator equation B(u) Γ€ f = 0 in a real Hilbert space. Let us call this equation ill-posed if the operator B 0 (u) is not boundedly invertible, and well-posed otherwise. The dynamical systems method (DSM) for solving this equation consists of a construction of 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 minimal-norm solution to the equation B(u) = f. A global convergence theorem is proved for DSM for equation B(u) Γ€ f = 0 with monotone C 2 loc operators B.

πŸ“œ SIMILAR VOLUMES

An implicit Landweber method for nonline
An implicit Landweber method for nonlinear ill-posed operator equations
✍ Wei Wang; Bo Han πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 455 KB

In this paper, we are interested in the solution of nonlinear inverse problems of the form F (x) = y. We propose an implicit Landweber method, which is similar to the third-order midpoint Newton method in form, and consider the convergence behavior of the implicit Landweber method. Using the discrep

An implicit method for linear ill-posed
An implicit method for linear ill-posed problems with perturbed operators
✍ Jian-guo Tang πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 119 KB

## Abstract An implicit iterative method is applied to solving linear ill‐posed problems with perturbed operators. It is proved that the optimal convergence rate can be obtained after choosing suitable number of iterations. A generalized Morozov's discrepancy principle is proposed for the problems,

A Runge–Kutta type modified Landweber me
A Runge–Kutta type modified Landweber method for nonlinear ill-posed operator equations
✍ W. Wang; B. Han; L. Li πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 189 KB

In this paper, we investigate the convergence behavior of a Runge-Kutta type modified Landweber method for nonlinear ill-posed operator equations. In order to improve the stability and convergence of the Landweber iteration, a 2-stage Gauss-type Runge-Kutta method is applied to the continuous analog