M.A. Krasnoselskii theorem and iteration methods of solving ill-posed linear problems with a self-adjoint operator

2014/12/03 by O. V. Matysik, Matysik, O. V., P. P. Zabreiko +1
Mathematics · #47A52 #65F22 #65Q30 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:47A52 #msc:65F22 #msc:65Q30

paper · pdf · doi:10.48550/arxiv.1412.1222

22 pages

arxiv created 2014/12/03 · arxiv updated 2014/12/04

Abstract

The article deals with iterative methods of solving linear operator equations x = Bx + f and Ax = f with self-adjoint operators in Hilbert space X in critical case when ρ(B) = 1 and 0 ∈ \rm Sp A. The main results are based on the use of M.A. Krasnosel'skiĭ theorem about the convergence of the successive approximations and some its modifications and refinements.

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