NII Technical Reports
National Institute of Informatics
| Title | Convergence of the Conjugate Gradient Method on Singular Systems |
| Authors | Ken Hayami |
| Abstract | 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. |
| Language | English |
| Published | July 29, 2018 |
| Pages | 7p |
| PDF File | 18-001E.pdf |