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A robust incomplete Choleski‐conjugate gradient algorithm
Author(s) -
Ajiz M. A.,
Jennings A.
Publication year - 1984
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.1620200511
Subject(s) - conjugate gradient method , convergence (economics) , conjugate residual method , coefficient matrix , mathematics , matrix (chemical analysis) , iterative method , rate of convergence , positive definite matrix , derivation of the conjugate gradient method , nonlinear conjugate gradient method , algorithm , sparse matrix , conjugate , mathematical optimization , computer science , gradient descent , mathematical analysis , artificial intelligence , computer network , channel (broadcasting) , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , artificial neural network , economics , composite material , gaussian , economic growth
When applied to large sparse sets of simultaneous equations, classical iterative methods may yield very poor convergence rates. This paper gives an incomplete Choleski‐conjugate gradient algorithm (ICCG) which has reliably good convergence rates at the expense of computing and using at each iteration an incomplete Choleski factor of the coefficient matrix. The method is applicable to any problems in which the coefficient matrix is symmetric positive definite and is likely to be advantageous with respect to elimination when it is not possible to represent the equations in a dense band form.