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

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

the problem ˙uδ(t) = −uδ(t) + T −1 a(t) A ∗ fδ, u(0) = u0, (∗) where T: = A ∗ A, Ta: = T + aI, and a = a(t)> 0, a(t) ց 0 as t → ∞ is suitably chosen. It is proved that uδ: = uδ(tδ) has the property limδ→0 ‖uδ − y ‖ = 0. Here the stopping time tδ is defined by the discrepancy principle: ∫ t 0 e −(t−s) a

A discrepancy principle for Poisson data

Analysis of an approximate model for Poisson data reconstruction and a related discrepancy principle This article has been downloaded from IOPscience. Please scroll down to see the full text article.

(normally available), in order to solve an ill-posed problem in a stable fashion. In this thesis, theoretical and numerical investigation of Tikhonov’s (variational) regularization is presented. The regularization parameter is computed by the discrepancy principle of Morozov, and a first-kind integral

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We investigate the discrepancy principle for choosing smoothing parameters for kernel density estimation. The method is based on the distance between the empirical and estimated distribution functions. We prove some new positive and negative results on L1-consistency of kernel estimators

by the generalized discrepancy principle. Under certain smoothness assumptions we provide order optimal error bounds that characterize the accuracy of the regularized solution. It appears that for getting small error bounds a proper scaling of the penalizing operator B is required. For the computation

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