The rate of convergence for the cyclic projections algorithm II: norms of nonlinear operators

Authors:
Frank Deutsch;Hein Hundal
Affiliations:
Department of Mathematics, Penn State University, University Park, PA;Port Matilda, PA
Venue:
Journal of Approximation Theory
Year:
2006

Citing 4
Cited 2

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A dual approach to constrained interpolation from a convex subset of Hilbert space

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Projection algorithms and monotone operators

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The rate of convergence for the cyclic projections algorithm I: angles between convex sets

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The rate of convergence for the cyclic projections algorithm I: angles between convex sets

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The rate of convergence for the cyclic projections algorithm III: Regularity of convex sets

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Abstract

The rate of convergence for the cyclic projections algorithm onto an intersection of finitely many closed convex sets in a Hilbert space is investigated. Recently we showed that this rate could be described in terms of the "angles" between the convex sets involved. Here we show that these angles may often be described in terms of the "norms" of certain nonlinear operators, and hence obtain an alternate way of computing this rate of convergence.