Reaching the superlinear convergence phase of the CG method

0438751 - ÚGN 2015 RIV NL eng J - Journal Article
Axelsson, Owe - Karátson, J.
Reaching the superlinear convergence phase of the CG method.
Journal of Computational and Applied Mathematics. Roč. 260, č. 260 (2014), s. 244-257. ISSN 0377-0427. E-ISSN 1879-1778
R&D Projects: GA MŠMT ED1.1.00/02.0070
Institutional support: RVO:68145535
Keywords : superlinear convergence * conjugate gradient method * eigenvalues
Subject RIV: BA - General Mathematics
Impact factor: 1.266, year: 2014
http://www.sciencedirect.com/science/article/pii/S0377042713005451

The rate of convergence of the conjugate gradient method takes place in essentially three phases, with respectively a sublinear, a linear and a superlinear rate. The paper examines when the superlinear phase is reached. To do this, two methods are used. One is based on the K-condition number, thereby separating the eigenvalues in three sets: small and large outliers and intermediate eigenvalues. The other is based on annihilating polynomials for the eigenvalues and, assuming various analytical distributions of them, thereby using certain refined estimates. The results are illustrated for some typical distributions of eigenvalues and with some numerical tests.
Permanent Link: http://hdl.handle.net/11104/0242127