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GPCG–generalized preconditioned CG method and its use with non‐linear and non‐symmetric displacement decomposition preconditioners
Author(s) -
Blaheta Radim
Publication year - 2002
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.295
Subject(s) - conjugate gradient method , mathematics , orthogonalization , derivation of the conjugate gradient method , conjugate residual method , linear system , generalization , multiplicative function , mathematical analysis , mathematical optimization , algorithm , computer science , gradient descent , machine learning , artificial neural network
The paper investigates a generalization of the preconditioned conjugate gradient method, which uses explicit orthogonalization of the search directions. This generalized preconditioned conjugate gradient (GPCG) method is suitable for solving the symmetric positive definite systems with preconditioners, which can be non‐symmetric or non‐linear . Such preconditioners can arise from computing of the pseudoresiduals by some additive or multiplicative space decomposition method with inexact solution of the auxiliary subproblems by inner iterations. The non‐linear and non‐symmetric preconditioners based on displacement decomposition for solving elasticity problems are described as an example of such preconditioners. Copyright © 2002 John Wiley & Sons, Ltd.