A General Convergence Analysis of Some Newton-Type Methods for Nonlinear Inverse Problems

We consider the methods xδ n+1 = xδ n − gαn (F (xδ n)∗F (xδ n))F (xδ n)∗(F (xδ n)− yδ) for solving nonlinear ill-posed inverse problems F (x) = y using the only available noise data yδ satisfying yδ − y ≤ δ with a given small noise level δ > 0. We terminate the iteration by the discrepancy principle F (xδ nδ )−yδ ≤ τδ < F (xδ

• Type: Journal
• Year: 2011
• Where: SIAMNUM
• Authors: Qinian Jin
• Keywords: Available Noise Data, Nonlinear Ill-posed Inverse, SIAMNUM 2011, Small Noise Level