We present a generalization to an arbitrary number of subspaces of the cosine of the Friedrichs angle between two subspaces of a Hilbert space. This parameter is used to analyze the rate of convergence in the von Neumann–Halperin method of alternating projections.
On considère une généralisation à plusieurs espaces du cosinus de l'angle de Friedrichs entre deux sous-espaces d'un espace de Hilbert. On utilise ce paramètre pour analyser la vitesse de convergence dans la méthode des projections alternées de von Neumann–Halperin.
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Catalin Badea 1; Sophie Grivaux 1; Vladimir Müller 2
@article{CRMATH_2010__348_1-2_53_0, author = {Catalin Badea and Sophie Grivaux and Vladimir M\"uller}, title = {A generalization of the {Friedrichs} angle and the method of alternating projections}, journal = {Comptes Rendus. Math\'ematique}, pages = {53--56}, publisher = {Elsevier}, volume = {348}, number = {1-2}, year = {2010}, doi = {10.1016/j.crma.2009.11.018}, language = {en}, }
TY - JOUR AU - Catalin Badea AU - Sophie Grivaux AU - Vladimir Müller TI - A generalization of the Friedrichs angle and the method of alternating projections JO - Comptes Rendus. Mathématique PY - 2010 SP - 53 EP - 56 VL - 348 IS - 1-2 PB - Elsevier DO - 10.1016/j.crma.2009.11.018 LA - en ID - CRMATH_2010__348_1-2_53_0 ER -
Catalin Badea; Sophie Grivaux; Vladimir Müller. A generalization of the Friedrichs angle and the method of alternating projections. Comptes Rendus. Mathématique, Volume 348 (2010) no. 1-2, pp. 53-56. doi : 10.1016/j.crma.2009.11.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.11.018/
[1] Theory of reproducing kernels, Trans. Amer. Math. Soc., Volume 68 (1950), pp. 337-404
[2] C. Badea, S. Grivaux, V. Müller, The rate of convergence in the method of alternating projections, preprint
[3] Characterizing arbitrarily slow convergence in the method of alternating projections | arXiv
[4] Best Approximation in Inner Product Spaces, CMS Books in Mathematics, vol. 7, Springer, New York, 2001
[5] Rate of convergence of the method of alternating projections, Parametric Optimization and Approximation, Internat. Schriftenreihe Numer. Math., vol. 72, Birkhäuser, Basel, 1985, pp. 96-107
[6] The rate of convergence for the method of alternating projections. II, J. Math. Anal. Appl., Volume 205 (1997), pp. 381-405
[7] The product of projection operators, Acta Sci. Math. (Szeged), Volume 23 (1962), pp. 96-99
[8] Error bounds for the method of alternating projections, Math. Control Signals Systems, Volume 1 (1988), pp. 43-59
[9] Treatise on the Shift Operator. Spectral Function Theory, Grundlehren der Mathematischen Wissenschaften, vol. 273, Springer-Verlag, Berlin, 1986 (Translated from the Russian by Jaak Peetre)
[10] The method of alternating projections and the method of subspace corrections in Hilbert space, J. Amer. Math. Soc., Volume 15 (2002), pp. 573-597
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