Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
756291 | Communications in Nonlinear Science and Numerical Simulation | 2008 | 8 Pages |
Abstract
Let Ay = f, A is a linear operator in a Hilbert space H, y ⊥ N(A) ≔ {u : Au = 0}, R(A) ≔ {h : h = Au, u ∈ D(A)} is not closed, ∥fδ − f∥ ⩽ δ. Given fδ, one wants to construct uδ such that limδ→0∥uδ − y∥ = 0. Two versions of discrepancy principles for the DSM (dynamical systems method) for finding the stopping time and calculating the stable solution uδ to the original equation Ay = f are formulated and mathematically justified.
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Authors
A.G. Ramm,