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Linear ill-posed problems and dynamical systems

Alexander G. Ramm
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Abstract

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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Alexander G. Ramm. 2001-10-19. Linear ill-posed problems and dynamical systems. https://arxiv.org/abs/math-ph/0008011

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