NII Technical Report (NII-2018-001E)

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

NII Technical Reports
National Institute of Informatics