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The present research work proposes a new fast fixed-point averaging algorithmon the compact Stiefel manifold based on a mixed retraction/lifting pair.Numerical comparisons between fixed-point algorithms based on the proposednon-associated retraction/lifting map pair and two associatedretraction/lifting pairs confirm that the averaging algorithm based on acombination of mixed maps is remarkably less computationally demanding than thesame averaging algorithm based on any of the constituent associatedretraction/lifting pairs.

Mixed Maps for Kolmogoroff-Nagumo-Type Averaging on the Compact Stiefel Manifold