The convergence behaviour of preconditioned CG and CG-S in the presence of rounding errors. (English) Zbl 0714.65034
Preconditioned conjugate gradient methods, Proc. Conf., Nijmegen/Neth. 1989, Lect. Notes Math. 1457, 126-136 (1990).
[For the entire collection see Zbl 0705.00024.]
It is analyzed why in the presence of roundoff errors the conjugate gradient (cg) method with modified incomplete Cholesky preconditioning is sometimes slower converging than the theoretically slower cg-method with incomplete Cholesky preconditioning. It is shown that this behaviour is due to a loss of orthogonality due to roundoff. Furthermore the convergence behaviour of the conjugate gradient squared method is analyzed and reasons for the irregular behaviour are given by analyzing an example.
It is analyzed why in the presence of roundoff errors the conjugate gradient (cg) method with modified incomplete Cholesky preconditioning is sometimes slower converging than the theoretically slower cg-method with incomplete Cholesky preconditioning. It is shown that this behaviour is due to a loss of orthogonality due to roundoff. Furthermore the convergence behaviour of the conjugate gradient squared method is analyzed and reasons for the irregular behaviour are given by analyzing an example.
Reviewer: V.Mehrmann
MSC:
| 65F10 | Iterative numerical methods for linear systems |
| 65F35 | Numerical computation of matrix norms, conditioning, scaling |
