Iterative regularization with minimum-residual methods
Iterative regularization with minimum-residual methods
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DOI：
10.1007/s10543-006-0109-5
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发表时间：
2007-01
影响因子：
1.5
通讯作者：
Toke Koldborg Jensen;P. Hansen
中科院分区：
文献类型：
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作者：
Toke Koldborg Jensen;P. Hansen
我们研究应用于离散不适定问题的迭代最小残差方法的正则化性质。在这些方法中，到底层 Krylov 子空间的投影充当正则化器，这项工作的重点是这些 Krylov 子空间的基向量所扮演的角色。我们提供了理论和数值示例的结合，我们的分析证实了 MINRES 和 MR-II 可以作为一般正则化方法的经验。我们还从理论上和实验上证明，一般来说，对于 GMRES 和 RRGMRES 来说，情况并非如此——它们作为正则化方法的成功高度依赖于问题。
We study the regularization properties of iterative minimum-residual methods applied to discrete ill-posed problems. In these methods, the projection onto the underlying Krylov subspace acts as a regularizer, and the emphasis of this work is on the role played by the basis vectors of these Krylov subspaces. We provide a combination of theory and numerical examples, and our analysis confirms the experience that MINRES and MR-II can work as general regularization methods. We also demonstrate theoretically and experimentally that the same is not true, in general, for GMRES and RRGMRES – their success as regularization methods is highly problem dependent.