A numerical study of various algorithms related to the preconditioned conjugate gradient method
Charles P. Jackson, PD Robinson · International Journal for Numerical Methods in Engineering · 1985
Abstract We present the results of a numerical study of the preconditioned conjugate gradient algorithm, the minimal residual algorithm, the biconjugate gradient algorithm and the bi‐minimal residual algorithm using both simple test matrices and more realistic test matrices derived from physical problems. The application of the methods to unsymmetric matrices is considered. We emphasize the importance of a good preconditioning, look at various methods including ICGG(n) and incomplete block factorization, and make some practical recommendations. Some of the folk‐lore surrounding the semi‐iterative methods is dispelled.