English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The Anderson Mixing (AM) method is a popular approach for acceleratingfixed-point iterations by leveraging historical information from previoussteps. In this paper, we introduce the Riemannian Anderson Mixing (RAM) method,an extension of AM to Riemannian manifolds, and analyze its local linearconvergence under reasonable assumptions. Unlike other extrapolation-basedalgorithms on Riemannian manifolds, RAM does not require computing the inverseretraction or inverse exponential mapping and has a lower per-iteration cost.Furthermore, we propose a variant of RAM called Regularized RAM (RRAM), whichestablishes global convergence and exhibits similar local convergenceproperties as RAM. Our proof relies on careful error estimations based on thelocal geometry of Riemannian manifolds. Finally, we present experimentalresults on various manifold optimization problems that demonstrate the superiorperformance of our proposed methods over existing Riemannian gradient descentand LBFGS approaches.

Riemannian Anderson Mixing Methods for Minimizing $C^2$-Functions on Riemannian Manifolds