Linear ill-posed problems and dynamical systems

Details Linear ill-posed problems and dynamical systems Linear ill-posed problems and dynamical systems

2000-08-03

arxiv.org/abs/math-ph/0008011v4

J.Math.Anal.Appl., 258, N1, (2001), 448-456

Physics

Mathematical Physics

Scientific paper

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.

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