English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the inexact Newton methods $$x_{n+1}^\d=x_n^\d-g_{\a_n}(F'(x_n^\d)^* F'(x_n^\d)) F'(x_n^\d)^*(F(x_n^\d)-y^\d) $$ for solving nonlinear ill-posed inverse problems $F(x)=y$using the only available noise data $y^\d$ satisfying $\|y^\d-y\|\le \d$ with agiven small noise level $\d>0$. We terminate the iteration by the discrepancyprinciple $$ \|F(x_{n_\d}^\d)-y^\d\|\le \tau \d<\|F(x_n^\d)-y^\d\|, \qquad 0\len<n_\d $$ with a given number $\tau>1$. Under certain conditions on $\{\a_n\}$and $F$, we prove for a large class of spectral filter functions $\{g_\a\}$ theconvergence of $x_{n_\d}^\d$ to a true solution as $\d\rightarrow 0$. Moreover,we derive the order optimal rates of convergence when certain H\"{o}lder sourceconditions hold. Numerical examples are given to test the theoretical results.

A general convergence analysis on inexact Newton method for nonlinear inverse problems