Linear ill-posed problems and dynamical systems
Ramm, Alexander G.
arXiv, 0008011 / Harvested from arXiv
Text on arXiv
A linear equation Au=f (1) with a bounded, injective, but not boundedly invertible linear operator in a Hilbert space H is studied. A new approach to solving linear ill-posed problems is proposed. The approach consists of solving a Cauchy problem for a linear equation in H, which is a dynamical system, proving the existence and uniqueness of its global solution u(t), and establishing that u(t) tends to a limit y, as t tends to infinity, and this limit y solves equation (1). The case when f in (1) is given with some error is also studied.
Publié le : 2000-08-03
Classification:  Mathematical Physics,  Mathematics - Analysis of PDEs,  Mathematics - Dynamical Systems,  Mathematics - Functional Analysis,  47A50, 47B05, 65M30 
@article{0008011,
     author = {Ramm, Alexander G.},
     title = {Linear ill-posed problems and dynamical systems},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0008011}
}

Ramm, Alexander G. Linear ill-posed problems and dynamical systems. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0008011/