2024-03-28T14:58:46Z
https://repository.nii.ac.jp/oai
oai:repository.nii.ac.jp:02000367
2023-01-11T05:53:16Z
136
NII Technical Report (NII-2018-001E):Convergence of the Conjugate Gradient Method on Singular Systems
速水, 謙
Hayami, Ken
テクニカルレポート
Technical Report
In this short paper, we analyze the convergence of the Conjugate Gradient (CG) method in exact arithmetic, when the coefficient matrix A is symmetric positive semidefinite and the system is consistent. To do so, we diagonalize A and decompose the algorithm into the range and the null space components of A. Further, we apply the analysis to the CGLS and CGNE (CG Normal Error) methods for rank-deficient least squares problems.
国立情報学研究所
2018-07-29
eng
departmental bulletin paper
https://doi.org/10.20736/0002000367
https://repository.nii.ac.jp/records/2000367
10.20736/0002000367
1346-5597
NIIテクニカル・レポート
NII Technical Report
1
7
https://repository.nii.ac.jp/record/2000367/files/18-001E.pdf
application/pdf
120 KB
2022-06-09