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Reaching the superlinear convergence phase of the CG method
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SYSNO ASEP 0438751 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Reaching the superlinear convergence phase of the CG method Author(s) Axelsson, Owe (UGN-S) RID
Karátson, J. (HU)Number of authors 2 Source Title Journal of Computational and Applied Mathematics. - : Elsevier - ISSN 0377-0427
Roč. 260, č. 260 (2014), s. 244-257Number of pages 14 s. Publication form Online - E Language eng - English Country NL - Netherlands Keywords superlinear convergence ; conjugate gradient method ; eigenvalues Subject RIV BA - General Mathematics R&D Projects ED1.1.00/02.0070 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) Institutional support UGN-S - RVO:68145535 UT WOS 000330821800022 DOI 10.1016/j.cam.2013.10.001 Annotation 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. Workplace Institute of Geonics Contact Lucie Gurková, lucie.gurkova@ugn.cas.cz, Tel.: 596 979 354 Year of Publishing 2015 Electronic address http://www.sciencedirect.com/science/article/pii/S0377042713005451
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