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A numerical study of various algorithms related to the preconditioned conjugate gradient method
Author(s) -
Jackson C. P.,
Robinson P. C.
Publication year - 1985
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620210711
Subject(s) - conjugate gradient method , biconjugate gradient method , residual , algorithm , conjugate residual method , mathematics , preconditioner , derivation of the conjugate gradient method , iterative method , nonlinear conjugate gradient method , gradient method , block (permutation group theory) , incomplete cholesky factorization , factorization , computer science , sparse matrix , geometry , gradient descent , artificial intelligence , artificial neural network , physics , quantum mechanics , gaussian
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.