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The convergence of projection on convex sets (POeS) algo rithms is monotonic and exponential near the point of con vergence, so it is reasonable to predict the limit point using a simple exponential regression. For circumstances where the convergence of each coordinate direction is, in fact, mono tonic, this results in signifi cant acceleration of poes. How ever, as we show, the convergence in the coordinates is not monotonic at points sufficiently far from the limit point. We develop an algorithm which takes direction changes into ac count. An example of poes on bandlimited reconstruction is presented.

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