Minimization of Tikhonov functionals in Banach spaces
Minimization of Tikhonov functionals in Banach spaces
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DOI：
10.1155/2008/192679
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发表时间：
2008-01-01
影响因子：
--
通讯作者：
Schuster, Thomas
中科院分区：
文献类型：
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作者：
Bonesky, Thomas;Kazimierski, Kamil S.;Schuster, Thomas
已知吉洪诺夫泛函非常适合于获得线性算子方程的正则解。我们分析了在Banach空间中寻找基于范数的Tikhonov泛函最小值的两种迭代方法。一种是最陡下降法，直接在底层空间中进行迭代，另一种是在对偶空间中进行迭代。证明了两种方法的强收敛性。版权所有(c) 2008托马斯·博内斯基等。
Tikhonov functionals are known to be well suited for obtaining regularized solutions of linear operator equations. We analyze two iterative methods for finding the minimizer of norm-based Tikhonov functionals in Banach spaces. One is the steepest descent method, whereby the iterations are directly carried out in the underlying space, and the other one performs iterations in the dual space. We prove strong convergence of both methods. Copyright (c) 2008 Thomas Bonesky et al.