An augmented LSQR method
An augmented LSQR method
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DOI：
10.1007/s11075-012-9665-8
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发表时间：
2012-12
影响因子：
2.1
通讯作者：
J. Baglama;L. Reichel;D. Richmond
中科院分区：
文献类型：
--
作者：
J. Baglama;L. Reichel;D. Richmond
用于求解最小二乘问题的LSQR迭代方法可能需要多次迭代以确定具有期望精度的近似解。这通常取决于与矩阵的小奇异值相关联的解的奇异向量分量需要多次迭代来确定的事实。用调和里兹向量增广Krylov子空间通常可以用比不增广时更少的迭代来确定与小奇异值相关联的奇异向量。本文描述了如何由LSQR迭代法生成的Krylov子空间可以方便地增加调和Ritz向量。计算实例表明了所提出的增广LSQR方法的竞争力。
The LSQR iterative method for solving least-squares problems may require many iterations to determine an approximate solution with desired accuracy. This often depends on the fact that singular vector components of the solution associated with small singular values of the matrix require many iterations to be determined. Augmentation of Krylov subspaces with harmonic Ritz vectors often makes it possible to determine the singular vectors associated with small singular values with fewer iterations than without augmentation. This paper describes how Krylov subspaces generated by the LSQR iterative method can be conveniently augmented with harmonic Ritz vectors. Computed examples illustrate the competitiveness of the augmented LSQR method proposed.