Projections onto convex sets: Difference between revisions

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The algorithm starts with an arbitrary value for <math>x_0</math> and then generate the sequence
 
: <math>x_{k+1} = \mathcal{P}_C \left( \mathcal{P}_D ( x_k ) \right). </math>.
 
The simplicity of the algorithm explains some of its popularity. If the [[Intersection (set theory)|intersection]] of ''C'' and ''D'' is non-empty, then the [[sequence]] generated by the algorithm will [[Convergent series|converge]] to some point in this intersection.