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Necessary and sufficient conditions for the existence of a conjugate gradient method

Journal Article · · SIAM J. Numer. Anal.; (United States)
DOI:https://doi.org/10.1137/0721026· OSTI ID:6682201

The authors characterize the class CG(s) of matrices A for which the linear system Ax = b can be solved by an s-term conjugate gradient method. The authors show that, except for a few anomalies, the class CG(s) consists of matrices A for which conjugate gradient methods are already known. These matrices are the Hermitian matrices, A* = A, and the matrices of the form A = e/sup i theta/(dI + B), with B* = -B. 7 references.

Research Organization:
Los Alamos National Lab., NM
OSTI ID:
6682201
Journal Information:
SIAM J. Numer. Anal.; (United States), Journal Name: SIAM J. Numer. Anal.; (United States) Vol. 21:2; ISSN SJNAA
Country of Publication:
United States
Language:
English

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