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Article overview
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Linear ill-posed problems and dynamical systems | Alexander G.Ramm
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3 Aug 2000 | Journal: | J.Math.Anal.Appl., 258, N1, (2001), 448-456 | Subject: | Mathematical Physics; Analysis of PDEs; Dynamical Systems; Functional Analysis MSC-class: 47A50, 47B05, 65M30 | math-ph math.AP math.DS math.FA math.MP | 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. | Source: | arXiv, math-ph/0008011 | Services: | Forum | Review | PDF | Favorites |
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