Block conjugate gradient methods
作者:
C.G. Broyden,
期刊:
Optimization Methods and Software
(Taylor Available online 1993)
卷期:
Volume 2,
issue 1
页码: 1-17
ISSN:1055-6788
年代: 1993
DOI:10.1080/10556789308805531
出版商: Gordon and Breach Science Publishers
关键词: Conjugate gradients;Conjugate directions;Block methods;Parallel computation
数据来源: Taylor
摘要:
In this paper a comprehensive theory is attempted of methods of conjugate-gradient type where the matrix of coefficients may be definite, indefinite or nonsymmetric. The theory is based on ‘leveling’ some underlying quadratic function over a linear manifold rather than just a straight line. It is shown that numerical instabilites occur when this quadratic Hessian is indefinite (well-known) or when another matrix employed, often implicitly, in the calculations is indefinite. The use of the various ‘look-ahead’ algorithms in combatting these instabilities is outlined and it is seen that this amounts to a ‘sequential block’ method. It is further shown that many well-known algorithms have ‘simultaneous block’ versions, where the size and composition of the initial blocks are essentially arbitrary. Since the columns of the individual blocks may be generated simultaneously rather than sequentially these methods lend themselves naturally to the techniques of parallel computation.
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