TY - JOUR
T1 - Convergence of an algorithm for finding the distance between a ball in a subspace and a sum of subspaces
AU - Ritov, Y.
PY - 1990
Y1 - 1990
N2 - Let S0,S1,...,Sk be all subspaces of a Hilbert space, and let S = S1⊕,..., ⊕Sk. An algorithm is investigated for finding members of S0 and S with the minimal angle between them. The algorithm is a modification of the alternating projection algorithm of von Neumann [Ann. of Math., 50(1949), 401-485; Functional Operators, The Geometry of Orthogonal Spaces, Ann. of Math Stud., 1950]. It is similar to the algorithm suggested by Brieman and Friedman [J. Amer. Statist. Assoc., 17(1985), pp. 580-598] without a proof. The convergence of the algorithm is proved to be exponentially fast.
AB - Let S0,S1,...,Sk be all subspaces of a Hilbert space, and let S = S1⊕,..., ⊕Sk. An algorithm is investigated for finding members of S0 and S with the minimal angle between them. The algorithm is a modification of the alternating projection algorithm of von Neumann [Ann. of Math., 50(1949), 401-485; Functional Operators, The Geometry of Orthogonal Spaces, Ann. of Math Stud., 1950]. It is similar to the algorithm suggested by Brieman and Friedman [J. Amer. Statist. Assoc., 17(1985), pp. 580-598] without a proof. The convergence of the algorithm is proved to be exponentially fast.
UR - http://www.scopus.com/inward/record.url?scp=0025502648&partnerID=8YFLogxK
U2 - 10.1137/0727078
DO - 10.1137/0727078
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AN - SCOPUS:0025502648
SN - 0036-1429
VL - 27
SP - 1355
EP - 1367
JO - SIAM Journal on Numerical Analysis
JF - SIAM Journal on Numerical Analysis
IS - 5
ER -