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Mixed maps for learning a Kolmogoroff-Nagumo-type average element on the compact Stiefel manifold

The present research work proposes a new fast fixed-point average-value learning algorithm on the compact Stiefel manifold based on a mixed retraction/lifting pair. Numerical comparisons between fixed-point algorithms based on the proposed non-associated retraction/lifting map pair and two associated retraction/lifting pairs confirm that the averaging algorithm based on a combination of mixed maps is remarkably less computationally demanding than the same averaging algorithm based on any of the constituent associated retraction/lifting pairs.