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Statements

Subject Item
n2:RIV%2F67985840%3A_____%2F09%3A00321374%21RIV09-AV0-67985840
rdf:type
n3:Vysledek skos:Concept
dcterms: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. 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.
dcterms:title
Do projections stay close together? Do projections stay close together? Zůstávají projekce pohromadě?
skos:prefLabel
Do projections stay close together? Do projections stay close together? Zůstávají projekce pohromadě?
skos:notation
RIV/67985840:_____/09:00321374!RIV09-AV0-67985840
n4:aktivita
n5:Z n5:P
n4:aktivity
P(GA201/06/0018), Z(AV0Z10190503)
n4:cisloPeriodika
2
n4:dodaniDat
n11:2009
n4:domaciTvurceVysledku
n10:8718105
n4:druhVysledku
n14:J
n4:duvernostUdaju
n18:S
n4:entitaPredkladatele
n8:predkladatel
n4:idSjednocenehoVysledku
311030
n4:idVysledku
RIV/67985840:_____/09:00321374
n4:jazykVysledku
n16:eng
n4:klicovaSlova
projection; iteration; Hilbert space
n4:klicoveSlovo
n6:iteration n6:Hilbert%20space n6:projection
n4:kodStatuVydavatele
US - Spojené státy americké
n4:kontrolniKodProRIV
[CF8DAE19EC55]
n4:nazevZdroje
Journal of Mathematical Analysis and Applications
n4:obor
n12:BA
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
3
n4:projekt
n15:GA201%2F06%2F0018
n4:rokUplatneniVysledku
n11:2009
n4:svazekPeriodika
350
n4:tvurceVysledku
Kopecká, Eva Müller, S. Kirchheim, B.
n4:wos
000261895900038
n4:zamer
n7:AV0Z10190503
s:issn
0022-247X
s:numberOfPages
13