Voir la notice de l'article provenant de la source Math-Net.Ru
@article{AA_2011_23_3_a0, author = {C. Badea and S. Grivaux and V. M\"uller}, title = {The rate of convergence in the method of alternating projections}, journal = {Algebra i analiz}, pages = {1--30}, publisher = {mathdoc}, volume = {23}, number = {3}, year = {2011}, language = {en}, url = {http://geodesic.mathdoc.fr/item/AA_2011_23_3_a0/} }
C. Badea; S. Grivaux; V. Müller. The rate of convergence in the method of alternating projections. Algebra i analiz, Tome 23 (2011) no. 3, pp. 1-30. http://geodesic.mathdoc.fr/item/AA_2011_23_3_a0/
[1] Amemiya I., Andô T., “Convergence of random products of contractions in Hilbert space”, Acta Sci. Math. (Szeged), 26 (1965), 239–244 | MR | Zbl
[2] Aronszajn N., “Theory of reproducing kernels”, Trans. Amer. Math. Soc., 68 (1950), 337–404 | DOI | MR | Zbl
[3] Badea C., Lyubich Yu. I., “Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces”, Studia Math., 201 (2010), 21–35 | DOI | MR | Zbl
[4] Badea C., Müller V., “On weak orbits of operators”, Topology Appl., 156 (2009), 1381–1385 | DOI | MR | Zbl
[5] Bauschke H. H., Deutsch F., Hundal H., Characterizing arbitrarily slow convergence in the method of alternating projections, arXiv: 0710.2387 | MR
[6] Bauschke H. H., Borwein J. M., “On projection algorithms for solving convex feasibility problems”, SIAM Rev., 38 (1996), 367–426 | DOI | MR | Zbl
[7] Bauschke H. H., Borwein J. M., Lewis A. S., “The method of cyclic projections for closed convex sets in Hilbert space”, Recent Developments in Optimization Theory and Nonlinear Analysis (Jerusalem, 1995), Contemp. Math., 204, Amer. Math. Soc., Providence, RI, 1997, 1–38 | MR | Zbl
[8] Berkson E., “Hermitian projections and orthogonality in Banach spaces”, Proc. London Math. Soc. (3), 24 (1972), 101–118 | DOI | MR | Zbl
[9] Bruck R. E., Reich S., “Nonexpansive projections and resolvents of accretive operators in Banach spaces”, Houston J. Math., 3 (1977), 459–470 | MR | Zbl
[10] Deutsch F., Best approximation in inner product spaces, CMS Books in Math., 7, Springer, New York, 2001 | MR | Zbl
[11] Deutsch F., “Rate of convergence of the method of alternating projections”, Parametric Optimization and Approximation (Oberwolfach, 1983), Internat. Schriftenreihe Numer. Math., 72, Birkhäuser, Basel, 1985, 96–107 | MR
[12] Deutsch F., “The angle between subspaces of a Hilbert space”, Approximation Theory, Wavelets and Applications (Maratea, 1994), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 454, Kluwer Acad. Publ., Dordrecht, 1995, 107–130 | MR | Zbl
[13] Deutsch F., Hundal H., “The rate of convergence for the method of alternating projections, II”, J. Math. Anal. Appl., 205 (1997), 381–405 | DOI | MR | Zbl
[14] Dye J., “Convergence of random products of compact contractions in Hilbert space”, Integral Equations Operator Theory, 12 (1989), 12–22 | DOI | MR | Zbl
[15] Dye J., Khamsi M. A., Reich S., “Random products of contractions in Banach spaces”, Trans. Amer. Math. Soc., 325 (1991), 87–99 | DOI | MR | Zbl
[16] Halperin I., “The product of projection operators”, Acta Sci. Math. (Szeged), 23 (1962), 96–99 | MR | Zbl
[17] Kayalar S., Weinert H., “Error bounds for the method of alternating projections”, Math. Control Signals Systems, 1 (1988), 43–59 | DOI | MR | Zbl
[18] Kato T., Perturbation theory for linear operators, Reprint of the 1980 edition, Classics in Math., Springer, Berlin, 1995 | MR
[19] Kirchheim B., Kopecká E., Müller S., “Do projections stay close together?”, J. Math. Anal. Appl., 350 (2009), 859–871 | DOI | MR | Zbl
[20] Katznelson Y., Tzafriri L., “On power bounded operators”, J. Funct. Anal., 68 (1986), 313–328 | DOI | MR | Zbl
[21] Krengel U., Ergodic theorems, de Gruyter Stud. Math., 6, Walter de Gruyter, Berlin, 1985 | MR | Zbl
[22] Lin M., “On the uniform ergodic theorem”, Proc. Amer. Math. Soc., 43 (1974), 337–340 | DOI | MR | Zbl
[23] Lindenstrauss J., Tzafriri L., Classical Banach spaces, v. I, II, Classics in Math., Springer, Berlin–New York, 1996 | MR
[24] Müller V., “Power bounded operators and supercyclic vectors”, Proc. Amer. Math. Soc., 131 (2003), 3807–3812 | DOI | MR
[25] Müller V., “Power bounded operators and supercyclic vectors, II”, Proc. Amer. Math. Soc., 133 (2005), 2997–3004 | DOI | MR
[26] Müller V., Spectral theory of linear operators and spectral systems in Banach algebras, Oper. Theory Adv. Appl., 139, Second ed., Birkhäuser, Basel, 2007 | MR
[27] von Neumann J., “On rings of operators. Reduction theory”, Ann. of Math. (2), 50 (1949), 401–485 | DOI | MR | Zbl
[28] Nikolskii N. K., Lektsii ob operatore sdviga, Nauka, M., 1980 ; Treatise on the shift operator. Spectral function theory, Grundlehren Math. Wiss., 273, Springer-Verlag, Berlin, 1986 | MR | MR
[29] Pierra G., “Decomposition through formalization in a product space”, Math. Programming, 28 (1984), 96–115 | DOI | MR | Zbl
[30] Sakai M., “Strong convergence of infinite products of orthogonal projections in Hilbert space”, Appl. Anal., 59 (1995), 109–120 | DOI | MR | Zbl
[31] Smith K. T., Solmon D. C., Wagner S. L., “Practical and mathematical aspects of the problem of reconstructing objects from radiographs”, Bull. Amer. Math. Soc., 83:6 (1977), 1227–1270 | DOI | MR | Zbl
[32] Xu J., Zikatanov L., “The method of alternating projections and the method of subspace corrections in Hilbert space”, J. Amer. Math. Soc., 15 (2002), 573–597 | DOI | MR | Zbl