V-cycle convergence of some multigrid methods for ill-posed problems
V-cycle convergence of some multigrid methods for ill-posed problems
复制标题
一些针对病态问题的多重网格方法的V循环收敛
DOI：
10.1090/s0025-5718-03-01533-3
复制
发表时间：
2003
期刊：
影响因子：
--
通讯作者：
B. Kaltenbacher
中科院分区：
文献类型：
--
作者：
B. Kaltenbacher
对于不适定的线性算子方程，我们考虑一些V-循环多重网格方法，在Bramble，Pasciak，Wang和Xu（1991）的框架下，我们证明了产生水平独立的收缩因子估计。因此，我们可以将这些多重网格运营商在一个完整的多重网格方法，与差异的原则，被证明是作为一个迭代正则化方法的基础无穷维不适定问题。数值实验验证了理论结果。
For ill-posed linear operator equations we consider some V-cycle multigrid approaches, that, in the framework of Bramble, Pasciak, Wang, and Xu (1991), we prove to yield level independent contraction factor estimates. Consequently, we can incorporate these multigrid operators in a full multigrid method, that, together with a discrepancy principle, is shown to act as an iterative regularization method for the underlying infinite-dimensional ill-posed problem. Numerical experiments illustrate the theoretical results.