Fetching the paper…
Reading the bibliography…
The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems, dynamic low-rank decompositions and model reduction.
C. Li, X. Wang, J. Wang, and J.-C. Yao · 1910
Earlier work this paper cites.
Zur Riemannschen Geometrie in Grassmannschen Mannigfaltigkeiten
K. Leichtweiss · 1961
Earlier work this paper cites.
Foundations of differential geometry. Vol. I & II
S. Kobayashi and K. Nomizu · 1963
Earlier work this paper cites.
Differential geometry of Grassmann manifolds
Y.-C. Wong · 1967
Earlier work this paper cites.
Conjugate loci in Grassmann manifolds
Y.-C. Wong · 1968
Earlier work this paper cites.
Sectional curvatures of Grassmann manifolds
Y.-C. Wong · 1968
Earlier work this paper cites.
Decomposition of cut loci
R. L. Bishop · 1977
Earlier work this paper cites.
On cut loci of compact symmetric spaces
T. Sakai · 1977
Earlier work this paper cites.
Semi-Riemannian geometry - With applications to relativity
B. O’Neill · 1983
Earlier work this paper cites.
Grassmannian manifolds as subsets of Euclidean spaces
A. Machado and I. Salavessa · 1985
Earlier work this paper cites.
A matrix inequality and its geometric applications
G. L. Wu and W. H. Chen · 1988
Earlier work this paper cites.
Grassmann manifolds and Grassmann image of submanifolds
A. A. Borisenko and Yu. A. Nikolaevskiĭ · 1991
Earlier work this paper cites.
Topics in matrix analysis
R. A. Horn and C. R. Johnson · 1991
Earlier work this paper cites.
Riemannian Geometry
M. P. do Carmo · 1992
Earlier work this paper cites.
Numerical Methods for Large Eigenvalue Problems
Y. Saad · 1992
Earlier work this paper cites.
Optimization and Dynamical Systems
U. Helmke and J. B. Moore · 1994
Earlier work this paper cites.
Riemannian Geometry
T. Sakai · 1996
Earlier work this paper cites.
On the geometry of complex Grassmann manifold, its noncompact dual and coherent states
S. Berceanu · 1997
Earlier work this paper cites.
The geometry of algorithms with orthogonality constraints
A. Edelman, T. A. Arias, and S. T. Smith · 1998
Earlier work this paper cites.
On smooth decompositions of matrices
L. Dieci and T. Eirola · 1999
Earlier work this paper cites.
Differential Geometry, Lie Groups, and Symmetric Spaces
S. Helgason · 2001
Earlier work this paper cites.
Geometry of real Grassmann manifolds. Part I - VI
E. S. Kozlov · 2001
Earlier work this paper cites.
Efficient algorithms for inferences on Grassmann manifolds
K. A. Gallivan, A. Srivastava, X. Liu, and P. Van Dooren · 2003
Earlier work this paper cites.
Riemannian geometry of Grassmann manifolds with a view on algorithmic computation
P.-A. Absil, R. Mahony, and R. Sepulchre · 2004
Earlier work this paper cites.
Tools for application-driven linear dimension reduction
A. Srivastava and X. Liu · 2004
Cited alongside, same era.
On the largest principal angle between random subspaces
P.-A. Absil, A. Edelman, and P. Koev · 2005
Cited alongside, same era.
Unitarily Invariant Metrics on the Grassmann Space
L. Qiu, Y. Zhang, and C.-K. Li · 2005
Cited alongside, same era.
Multiscale representations for manifold-valued data
I. U. Rahman, I. Drori, V. C. Stodden, D. L. Donoho, and P. Schröder · 2005
Cited alongside, same era.
Geometric numerical integration
E. Hairer, C. Lubich, and G. Wanner · 2006
Cited alongside, same era.
Newton’s method on Graßmann manifolds, 2007
U. Helmke, K. Hüper, and J. Trumpf · 2007
Cited alongside, same era.
Lie Groups and Geometric Aspects of Isometric Actions
M. M. Alexandrino and R. G. Bettiol · 2015
Later among the works it cites.
Local convergence of an algorithm for subspace identification from partial data
L. Balzano and S. J. Wright · 2015
Later among the works it cites.
Low-rank matrix completion via preconditioned optimization on the Grassmann manifold
N. Boumal and P.-A. Absil · 2015
Later among the works it cites.
Lie Groups, Lie Algebras, and Representations: An Elementary Introduction
B. C. Hall · 2015
Later among the works it cites.
Model order reduction of parameterized circuit equations based on interpolation
T. S. Nguyen and T. Stykel · 2015
Later among the works it cites.
Riemannian computing in computer vision
A. Srivastava and P. K. Turaga · 2015
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Dynamical low‐rank approximation
O. Koch and C. Lubich · 2007
Cited alongside, same era.
Optimization Algorithms on Matrix Manifolds
P.-A. Absil, R. Mahony, and R. Sepulchre · 2008
Cited alongside, same era.
Interpolation method for adapting reduced-order models and application to aeroelasticity
D. Amsallem and C. Farhat · 2008
Cited alongside, same era.
Functions of Matrices: Theory and Computation
N. J. Higham · 2008
Cited alongside, same era.
Local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition
A. Hay, J. T. Borggaard, and D. Pelletier · 2009
Cited alongside, same era.
Simpler Grassmannian optimization, 2020
Z. Lai, L.-H. Lim, and K. Ye · 2009
Cited alongside, same era.
Algorithmic Advances in Riemannian Geometry and Applications: For Machine Learning, Computer Vision, Statistics, and Optimization
H. Q. Minh and V. Murino · 2016
Later among the works it cites.
Schubert varieties and distances between subspaces of different dimensions
K. Ye and L.-H. Lim · 2016
Later among the works it cites.
Global Convergence of a Grassmannian Gradient Descent Algorithm for Subspace Estimation
D. Zhang and L. Balzano · 2016
Later among the works it cites.
First-order methods for geodesically convex optimization
H. Zhang and S. Sra · 2016
Later among the works it cites.
Introduction to the Theory of Lie Groups
R. Godement and U. Ray · 2017
Later among the works it cites.
A Variational Model for Data Fitting on Manifolds by Minimizing the Acceleration of a Bézier Curve
R. Bergmann and P.-Y. Gousenbourger · 2018
Later among the works it cites.
Introduction to Riemannian Manifolds
J. M. Lee · 2018
Later among the works it cites.
Geometric subspace updates with applications to online adaptive nonlinear model reduction
R. Zimmermann, B. Peherstorfer, and K. Willcox · 2018
Later among the works it cites.
Statistics on the Stiefel manifold: Theory and applications
R. Chakraborty and B. C. Vemuri · 2019
Later among the works it cites.
Variations on a Theme of Schubert Calculus
M. Gillespie · 2019
Later among the works it cites.
Data fitting on manifolds with composite bézier-like curves and blended cubic splines
P.-Y. Gousenbourger, E. Massart, and P.-A. Absil · 2019
Later among the works it cites.
Hermite interpolation and data processing errors on Riemannian matrix manifolds
R. Zimmermann · 2020
Closest in time.
Momentum improves optimization on Riemannian manifolds
F. Alimisis, A. Orvieto, G. Becigneul, and A. Lucchi · 2021
Closest in time.
Manifold interpolation
R. Zimmermann · 2021
Closest in time.
F. Alimisis and B. Vandereycken · 2023
Closest in time.
Curvature and complexity: Better lower bounds for geodesically convex optimization, 2023
C. Criscitiello and N. Boumal · 2023
Closest in time.
Algorithms for data fitting on some common homogeneous spaces
Q. Rentmeesters · 2078
Closest in time.