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

TL;DR

This paper introduces a fast fixed-point averaging algorithm on the compact Stiefel manifold using a novel mixed retraction/lifting pair, significantly reducing computational complexity compared to traditional methods.

Contribution

It presents a new mixed retraction/lifting approach for averaging on the Stiefel manifold, improving efficiency over existing associated pairs.

Findings

Mixed maps reduce computational demand

Numerical results confirm efficiency gains

Algorithm maintains accuracy with less computation

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.