NII Technical Reports
National Institute of Informatics
| Title | GMRES on singular systems revisited |
| Authors | Ken Hayami and Kota Sugihara |
| Abstract | 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. |
| Language | English |
| Published | Sep 10, 2020 |
| Pages | 13p |
| PDF File | 20-004E.pdf |