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

Abstract

The present research work proposes a new fast fixed-point averaging 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.