2000/08/31 by Alexander G. Ramm
Physics and Astronomy · Mathematics · #math-ph #math.AP #math.DS #math.FA #math.MP #msc:47A50 #msc:47B05 #msc:65M30
published as J.Math.Anal.Appl., 258, N1, (2001), 448-456
arxiv created 2001/10/19 · arxiv updated 2009/11/30
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.