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| ESTIMATION OF THE CONVERGENCE RATE OF DYKSTRA'S CYCLIC PROJECTIONS ALGORITHM IN POLYHEDRAL CASE | |
| 作者姓名： | 许树声 |
| 摘 要： | 1.MainResultsAssumethatXisaHilbertspace.Fori=1,',r(r>1),assumeci∈R,fi∈Xwith||fi||=1,andKi={x∈X|(x,fi)≤ci},Hi={x∈X|(x,fi)=ci},K=∩Ki'i=1AboutthebackgroundofDykstra'scyclicprojectionsalgorithmoffindingPK(x),thebestapproximationtoagivenxEXinK,seethereferencesl-4].Recently,DeutschandHundal5]provedthatthesequence{xn}generatedbyDykstra'salgorithmhasaconvergencerateofexponentialtype.Ormoreexactly,||xn.-PK(x)||≤Pcn,n=0,1,',(l)wherepandcareconstantswithp>0,0≤c<1.AndifKistheinter… |
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