  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.
