On regularizing effects of MINRES and MR-II for large scale symmetric discrete ill-posed problems

@article{Huang2017OnRE,
  title={On regularizing effects of MINRES and MR-II for large scale symmetric discrete ill-posed problems},
  author={Yi Huang and Zhongxiao Jia},
  journal={J. Computational Applied Mathematics},
  year={2017},
  volume={320},
  pages={145-163}
}
Abstract. For large-scale symmetric discrete ill-posed problems, MR-II, a minimal residual method, is a competitive alternative to LSQR and CGLS. In this paper, we establish bounds for the distance between an underlying k-dimensional Krylov subspace and the subspace spanned by the k dominant eigenvectors. They show that the k-step MR-II captures the k dominant spectral components better for severely and moderately ill-posed problems than for mildly ill-posed problems, so that MR-II has better… CONTINUE READING
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