Predicting the behavior of finite precision Lanczos and conjugate gradient computations
SIAM Journal on Matrix Analysis and Applications
Iterative solution methods
SIAM Journal on Matrix Analysis and Applications
Conditioning analysis of separate displacement preconditioners for some nonlinear elasticity systems
Mathematics and Computers in Simulation
A novel, parallel PDE solver for unstructured grids
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Hi-index | 0.00 |
When solving linear systems and, in particular when solving large scale ill-conditioned problems it is important to understand the behaviour of the conjugate gradient method. The conjugate gradient method converges typically in three phases, an initial phase of rapid convergence but short duration, which depends essentially only on the initial error, a fairly linearly convergent phase, which depends on the spectral condition number and finally a superlinearly convergent phase, which depends on how the smallest eigenvalues are distributed. In the paper, this is explained by proper estimates of the rate of convergence.