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  • 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.
  • 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. (en)
Title
  • Reaching the superlinear convergence phase of the CG method
  • Reaching the superlinear convergence phase of the CG method (en)
skos:prefLabel
  • Reaching the superlinear convergence phase of the CG method
  • Reaching the superlinear convergence phase of the CG method (en)
skos:notation
  • RIV/68145535:_____/14:00438751!RIV15-AV0-68145535
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • I, P(ED1.1.00/02.0070)
http://linked.open...iv/cisloPeriodika
  • 260
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
  • Axelsson, Owe
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 41415
http://linked.open...ai/riv/idVysledku
  • RIV/68145535:_____/14:00438751
http://linked.open...riv/jazykVysledku
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  • superlinear convergence; conjugate gradient method; eigenvalues (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • NL - Nizozemsko
http://linked.open...ontrolniKodProRIV
  • [19E102DF629D]
http://linked.open...i/riv/nazevZdroje
  • Journal of Computational and Applied Mathematics
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 260
http://linked.open...iv/tvurceVysledku
  • Axelsson, Owe
  • Karátson, J.
issn
  • 0377-0427
number of pages
http://bibframe.org/vocab/doi
  • 10.1016/j.cam.2013.10.001
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