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Description
  • Článek se zabývá rychlostí konvergence iterací projekcí na K přímek v Hilbertově prostoru. Výsledek je dán do souvislosti s otázkou konvergence iterací projekci na K podprostoru Hilbertova prostoru. (cs)
  • We estimate the rate of convergence of products of projections on K intersecting lines in the Hilbert space. More generally, consider the orbit of a point under any sequence of orthogonal projections on K arbitrary lines in Hilbert space. Assume that the sum of the squares of the distances of the consecutive iterates is less than epsilon. We show that if epsilon tends to zero, then the diameter of the orbit tends to zero uniformly for all families of a fixed number K of lines. We relate this result to questions concerning convergence of products of projections on finite families of closed subspaces of the Hilbert space.
  • We estimate the rate of convergence of products of projections on K intersecting lines in the Hilbert space. More generally, consider the orbit of a point under any sequence of orthogonal projections on K arbitrary lines in Hilbert space. Assume that the sum of the squares of the distances of the consecutive iterates is less than epsilon. We show that if epsilon tends to zero, then the diameter of the orbit tends to zero uniformly for all families of a fixed number K of lines. We relate this result to questions concerning convergence of products of projections on finite families of closed subspaces of the Hilbert space. (en)
Title
  • Do projections stay close together?
  • Do projections stay close together? (en)
  • Zůstávají projekce pohromadě? (cs)
skos:prefLabel
  • Do projections stay close together?
  • Do projections stay close together? (en)
  • Zůstávají projekce pohromadě? (cs)
skos:notation
  • RIV/67985840:_____/09:00321374!RIV09-AV0-67985840
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/06/0018), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika
  • 2
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 311030
http://linked.open...ai/riv/idVysledku
  • RIV/67985840:_____/09:00321374
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • projection; iteration; Hilbert space (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [CF8DAE19EC55]
http://linked.open...i/riv/nazevZdroje
  • Journal of Mathematical Analysis and Applications
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
  • 350
http://linked.open...iv/tvurceVysledku
  • Kopecká, Eva
  • Müller, S.
  • Kirchheim, B.
http://linked.open...ain/vavai/riv/wos
  • 000261895900038
http://linked.open...n/vavai/riv/zamer
issn
  • 0022-247X
number of pages
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