The order of convergence for Landweber Scheme with $\alpha,\beta$-rule
2012
The Landweber scheme is widely used in various image reconstruction problems.
In previous works, $\alpha,\beta$-rule is suggested to stop the
Landweber iteration so as to get proper iteration results. The order of
convergence of discrepancy principal (DP rule), which is a special
case of $\alpha,\beta$-rule, with constant relaxation coefficient
$\lambda$ satisfying
$0 0)$ has been studied.
A sufficient condition for convergence of Landweber scheme is that
the value $\lambda_m\sigma_1^2$ should be lied in a closed interval,
i.e. $0<\varepsilon\leq\lambda_m\sigma_1^2\leq2-\varepsilon$,
$(0<\varepsilon<1)$. In this paper, we mainly investigate the order
of convergence of the $\alpha,\beta$-rule with variable relaxation
coefficient $\lambda_m$ satisfying $0 < \varepsilon\leq\lambda_m
\sigma_1^2 \leq 2-\varepsilon$. According to the order of
convergence, we can conclude that $\alpha,\beta$-rule is the optimal
rule for the Landweber scheme.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
19
References
0
Citations
NaN
KQI