Mathematical Programming
0025-5610
1436-4646
1976-12-01
en
articles
Some convergence properties of the conjugate gradient method
http://link.springer.com/10.1007%2FBF01580369
false
research_article
https://scigraph.springernature.com/explorer/license/
1976-12
2019-04-11T13:29
It has been conjectured that the conjugate gradient method for minimizing functions of several variables has a superlinear rate of convergence, but Crowder and Wolfe show by example that the conjecture is false. Now the stronger result is given that, if the objective function is a convex quadratic and if the initial search direction is an arbitrary downhill direction, then either termination occurs or the rate of convergence is only linear, the second possibility being more usual. Relations between the starting point and the initial search direction that are necessary and sufficient for termination in the quadratic case are studied.
42-49
dimensions_id
pub.1005266469
doi
10.1007/bf01580369
11
1
Pure Mathematics
Powell
M. J. D.
Mathematical Sciences
Springer Nature - SN SciGraph project
readcube_id
191764408d80a10a4262af4da16292e0123095389baa5bc08c423bcec2f7b533
University of Cambridge, Cambridge, United Kingdom
University of Cambridge