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Note on a modified Conjugate Gradient Method
Author(s) -
Wood Winifred L.
Publication year - 1973
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.1620070213
Subject(s) - conjugate gradient method , conjugate , derivation of the conjugate gradient method , nonlinear conjugate gradient method , conjugate residual method , property (philosophy) , mathematics , biconjugate gradient method , matrix (chemical analysis) , terminal (telecommunication) , set (abstract data type) , mathematical analysis , gradient method , pure mathematics , computer science , algorithm , gradient descent , materials science , artificial intelligence , philosophy , telecommunications , epistemology , artificial neural network , composite material , programming language
Mr. Bruce Irons recently 1 proposed a modification of the Conjugate Gradient Method. This note shows that if the matrix of the original set of equations is symmetric this method will have the same terminal property as the usual Conjugate Gradient Method except for a particular case when it will not converge at all. If the matrix is not symmetric we cannot deduce the usual terminal property.