Convergence of the Conjugate Gradient Method on Singular Systems
Numerical Analysis
2020-05-12 v2 Numerical Analysis
Abstract
We analyze the convergence of the Conjugate Gradient (CG) method in exact arithmetic, when the coefficient matrix is symmetric positive semidefinite and the system is consistent. To do so, we diagonalize and decompose the algorithm into the range and the null space components of . Further, we apply the analysis to the CGLS and CGNE (CG Normal Error) methods for rank-deficient least squares problems.
Cite
@article{arxiv.1809.00793,
title = {Convergence of the Conjugate Gradient Method on Singular Systems},
author = {Ken Hayami},
journal= {arXiv preprint arXiv:1809.00793},
year = {2020}
}
Comments
7 pages. NII Technical Report (NII-2018-001E) https://www.nii.ac.jp/TechReports/public_html/18-001E.html p.1, MSC number changed, Introduction, line 6 typo fixed. p. 3, bottom line 5-3: Comment added. p.6 Acknowledgement detail changed. p.7, 4 references added