@article{oai:repository.nii.ac.jp:02000372,
author = {速水, 謙 and Hayami, Ken and 杉原, 光太 and Sugihara, Kota},
journal = {NIIテクニカル・レポート, NII Technical Report},
month = {Sep},
note = {In [Hayami K, Sugihara M. Numer Linear Algebra Appl. 2011; 18:449--469], the authors analyzed the convergence behaviour of the Generalized Minimal Residual (GMRES) method for the least squares problem $ \min_{x \in R^n} {\| b - A x \|_2}^2$, where $ A \in R^{nxn}$ may be singular and $ b \in R^n, by decomposing the algorithm into the range $ R(A) $ and its orthogonal complement $ R(A)^\perp $ components. However, we found that the proof of the fact that GMRES gives a least squares solution if $ R(A) = R(A^T) $ was not complete. In this paper, we will give a complete proof.},
pages = {1--13},
title = {NII Technical Report (NII-2020-004E)：GMRES on singular systems revisited},
year = {2020}
}