메뉴 건너뛰기




Volumn 262, Issue 1, 2012, Pages 400-408

There is no variational characterization of the cycles in the method of periodic projections

Author keywords

Alternating projections; Best approximation; Limit cycle; Von Neumann algorithm

Indexed keywords


EID: 80955144168     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2011.09.002     Document Type: Article
Times cited : (36)

References (26)
  • 1
    • 0013467971 scopus 로고
    • Convergence of random products of contractions in Hilbert space
    • Amemiya I., Ando T. Convergence of random products of contractions in Hilbert space. Acta Sci. Math. (Szeged) 1965, 26:239-244.
    • (1965) Acta Sci. Math. (Szeged) , vol.26 , pp. 239-244
    • Amemiya, I.1    Ando, T.2
  • 2
    • 79955018270 scopus 로고    scopus 로고
    • On the random product of orthogonal projections in Hilbert space
    • World Scientific, River Edge, NJ
    • Baillon J.-B., Bruck R.E. On the random product of orthogonal projections in Hilbert space. Nonlinear Analysis and Convex Analysis 1999, 126-133. World Scientific, River Edge, NJ.
    • (1999) Nonlinear Analysis and Convex Analysis , pp. 126-133
    • Baillon, J.-B.1    Bruck, R.E.2
  • 3
    • 0000746478 scopus 로고
    • A norm convergence result on random products of relaxed projections in Hilbert space
    • Bauschke H.H. A norm convergence result on random products of relaxed projections in Hilbert space. Trans. Amer. Math. Soc. 1995, 347:1365-1373.
    • (1995) Trans. Amer. Math. Soc. , vol.347 , pp. 1365-1373
    • Bauschke, H.H.1
  • 4
    • 0001448913 scopus 로고
    • On the convergence of von Neumann's alternating projection algorithm for two sets
    • Bauschke H.H., Borwein J.M. On the convergence of von Neumann's alternating projection algorithm for two sets. Set-Valued Anal. 1993, 1:185-212.
    • (1993) Set-Valued Anal. , vol.1 , pp. 185-212
    • Bauschke, H.H.1    Borwein, J.M.2
  • 5
    • 0037976260 scopus 로고
    • Dykstra's alternating projection algorithm for two sets
    • Bauschke H.H., Borwein J.M. Dykstra's alternating projection algorithm for two sets. J. Approx. Theory 1994, 79:418-443.
    • (1994) J. Approx. Theory , vol.79 , pp. 418-443
    • Bauschke, H.H.1    Borwein, J.M.2
  • 6
    • 0002351732 scopus 로고    scopus 로고
    • The method of cyclic projections for closed convex sets in Hilbert space
    • Bauschke H.H., Borwein J.M., Lewis A.S. The method of cyclic projections for closed convex sets in Hilbert space. Contemp. Math. 1997, 204:1-38.
    • (1997) Contemp. Math. , vol.204 , pp. 1-38
    • Bauschke, H.H.1    Borwein, J.M.2    Lewis, A.S.3
  • 8
    • 2942687455 scopus 로고    scopus 로고
    • Finding best approximation pairs relative to two closed convex sets in Hilbert spaces
    • Bauschke H.H., Combettes P.L., Luke D.R. Finding best approximation pairs relative to two closed convex sets in Hilbert spaces. J. Approx. Theory 2004, 127:178-192.
    • (2004) J. Approx. Theory , vol.127 , pp. 178-192
    • Bauschke, H.H.1    Combettes, P.L.2    Luke, D.R.3
  • 9
    • 79955024543 scopus 로고    scopus 로고
    • On the random product of orthogonal projections in Hilbert space II
    • Bruck R.E. On the random product of orthogonal projections in Hilbert space II. Contemp. Math. 2010, 513:65-98.
    • (2010) Contemp. Math. , vol.513 , pp. 65-98
    • Bruck, R.E.1
  • 11
    • 0028543165 scopus 로고
    • Inconsistent signal feasibility problems: Least-squares solutions in a product space
    • Combettes P.L. Inconsistent signal feasibility problems: Least-squares solutions in a product space. IEEE Trans. Signal Process. 1994, 42:2955-2966.
    • (1994) IEEE Trans. Signal Process. , vol.42 , pp. 2955-2966
    • Combettes, P.L.1
  • 12
    • 13244295576 scopus 로고    scopus 로고
    • Solving monotone inclusions via compositions of nonexpansive averaged operators
    • Combettes P.L. Solving monotone inclusions via compositions of nonexpansive averaged operators. Optimization 2004, 53:475-504.
    • (2004) Optimization , vol.53 , pp. 475-504
    • Combettes, P.L.1
  • 13
    • 0001770096 scopus 로고
    • The method of alternating orthogonal projections
    • Kluwer, The Netherlands, S.P. Singh (Ed.)
    • Deutsch F. The method of alternating orthogonal projections. Approximation Theory, Spline Functions and Applications 1992, 105-121. Kluwer, The Netherlands. S.P. Singh (Ed.).
    • (1992) Approximation Theory, Spline Functions and Applications , pp. 105-121
    • Deutsch, F.1
  • 14
    • 0000876601 scopus 로고
    • Random products of nonexpansive mappings
    • Longman, Harlow, UK
    • Dye J., Reich S. Random products of nonexpansive mappings. Optimization and Nonlinear Analysis 1992, 106-118. Longman, Harlow, UK.
    • (1992) Optimization and Nonlinear Analysis , pp. 106-118
    • Dye, J.1    Reich, S.2
  • 15
    • 80955143136 scopus 로고    scopus 로고
    • Closed Fejer cycles for inconsistent systems of convex inequalities
    • Eremin I.I., Popov L.D. Closed Fejer cycles for inconsistent systems of convex inequalities. Russian Math. (Iz. VUZ) 2008, 52:8-16.
    • (2008) Russian Math. (Iz. VUZ) , vol.52 , pp. 8-16
    • Eremin, I.I.1    Popov, L.D.2
  • 17
    • 33845708830 scopus 로고
    • The method of projections for finding the common point of convex sets
    • Gubin L.G., Polyak B.T., Raik E.V. The method of projections for finding the common point of convex sets. Comput. Math. Math. Phys. 1967, 7:1-24.
    • (1967) Comput. Math. Math. Phys. , vol.7 , pp. 1-24
    • Gubin, L.G.1    Polyak, B.T.2    Raik, E.V.3
  • 18
    • 0002477272 scopus 로고
    • The product of projection operators
    • Halperin I. The product of projection operators. Acta Sci. Math. (Szeged) 1962, 23:96-99.
    • (1962) Acta Sci. Math. (Szeged) , vol.23 , pp. 96-99
    • Halperin, I.1
  • 19
    • 2042504393 scopus 로고    scopus 로고
    • An alternating projection that does not converge in norm
    • Hundal H.S. An alternating projection that does not converge in norm. Nonlinear Anal. 2004, 57:35-61.
    • (2004) Nonlinear Anal. , vol.57 , pp. 35-61
    • Hundal, H.S.1
  • 20
    • 33646672554 scopus 로고    scopus 로고
    • A note on the von Neumann alternating projections algorithm
    • Kopecká E., Reich S. A note on the von Neumann alternating projections algorithm. J. Nonlinear Convex Anal. 2004, 5:379-386.
    • (2004) J. Nonlinear Convex Anal. , vol.5 , pp. 379-386
    • Kopecká, E.1    Reich, S.2
  • 21
    • 80955144565 scopus 로고
    • Über die sukzessive Wahl des kürzesten Weges
    • Springer-Verlag, Berlin, O. Opitz, B. Rauhut (Eds.)
    • Kosmol P. Über die sukzessive Wahl des kürzesten Weges. Ökonomie und Mathematik 1987, 35-42. Springer-Verlag, Berlin. O. Opitz, B. Rauhut (Eds.).
    • (1987) Ökonomie und Mathematik , pp. 35-42
    • Kosmol, P.1
  • 24
    • 0001363448 scopus 로고
    • On rings of operators. Reduction theory
    • (the result in question was used by the author in his 1935 Princeton Lecture Notes; see also Theorem 13.7 in: J. von Neumann, Functional Operators II - The Geometry of Orthogonal Spaces, Ann. of Math. Stud., vol. 22, Princeton University Press, Princeton, NJ, 1950)
    • von Neumann J. On rings of operators. Reduction theory. Ann. of Math. 1949, 50:401-485. (the result in question was used by the author in his 1935 Princeton Lecture Notes; see also Theorem 13.7 in: J. von Neumann, Functional Operators II - The Geometry of Orthogonal Spaces, Ann. of Math. Stud., vol. 22, Princeton University Press, Princeton, NJ, 1950).
    • (1949) Ann. of Math. , vol.50 , pp. 401-485
    • von Neumann, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.