Convex Tikhonov regularization in Banach spaces: New results on convergence rates
Convex Tikhonov regularization in Banach spaces: New results on convergence rates
复制标题
Banach 空间中的凸 Tikhonov 正则化：收敛率的新结果
DOI：
10.1515/jiip-2015-0038
复制
发表时间：
2015
影响因子：
1.1
通讯作者：
S. Kindermann
中科院分区：
文献类型：
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作者：
S. Kindermann
摘要研究了Banach空间中线性不适定算子方程带凸罚项和凸保真度项的Tikhonov正则化。作为一个主要的结果，收敛速度的正则解的精确解的Bregman距离证明了通过施加一个推广的变分不等式条件的精确解。该条件仅涉及罚泛函之差在残差方面的衰减率。
Abstract Tikhonov regularization in Banach spaces with convex penalty and convex fidelity term for linear ill-posed operator equations is studied. As a main result, convergence rates in terms of the Bregman distance of the regularized solution to the exact solution is proven by imposing a generalization of the established variational inequality conditions on the exact solution. This condition only involves a decay rate of the difference of the penalty functionals in terms of the residual.