منابع مشابه
Discrepancy principle for DSM II
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 for...
متن کاملDiscrepancy principle for DSM
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, f δ − f ≤ δ. Given f δ , one wants to construct u δ such that lim δ→0 u δ − y = 0. A version of the DSM (dynamical systems method) for finding u δ consists of solving the problem ˙ u δ (t) = −u δ (t) + T −1 a(t) A * f δ , u(0) = u 0 , (*) where T := A * A, T a := T ...
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A simple proof of the convergence of the variational regularization, with the regularization parameter, chosen by the discrepancy principle, is given for linear operators under suitable assumptions. It is shown that the discrepancy principle, in general, does not yield uniform with respect to the data convergence. An a priori choice of the regularization parameter is proposed and justified for ...
متن کاملA new discrepancy principle
The aim of this note is to prove a new discrepancy principle. The advantage of the new discrepancy principle compared with the known one consists of solving a minimization problem (see problem (2) below) approximately, rather than exactly, and in the proof of a stability result. To explain this in more detail, let us recall the usual discrepancy principle, which can be stated as follows. Consid...
متن کاملDiscrepancy principle for the dynamical systems method
1 Discrepancy principle for the dynamical systems method Abstract Assume that Au = f, (1) is a solvable linear equation in a Hilbert space, ||A|| < ∞, and R(A) is not closed, so problem (1) is ill-posed. Here R(A) is the range of the linear operator A. A DSM (dynamical systems method) for solving (1), consists of solving the following Cauchy problem: ˙ u = −u + (B + (t)) −1 A * f, u(0) = u 0 , ...
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ژورنال
عنوان ژورنال: Communications in Nonlinear Science and Numerical Simulation
سال: 2008
ISSN: 1007-5704
DOI: 10.1016/j.cnsns.2006.11.006