Riemannian Geometry of Grassmann Manifolds with a View on Algorithmic Computation
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[1] I. Holopainen. Riemannian Geometry , 1927, Nature.
[2] K. Nomizu. Invariant Affine Connections on Homogeneous Spaces , 1954 .
[3] K. Leichtweiss. Zur Riemannschen Geometrie in Grassmannschen Mannigfaltigkeiten , 1961 .
[4] K. Nomizu,et al. Foundations of Differential Geometry , 1963 .
[5] Y. Wong. Differential geometry of grassmann manifolds. , 1967, Proceedings of the National Academy of Sciences of the United States of America.
[6] D. Luenberger. Optimization by Vector Space Methods , 1968 .
[7] G. Stewart. Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems , 1973 .
[8] W. Boothby. An introduction to differentiable manifolds and Riemannian geometry , 1975 .
[9] H. Karcher. Riemannian center of mass and mollifier smoothing , 1977 .
[10] S. Helgason. Differential Geometry, Lie Groups, and Symmetric Spaces , 1978 .
[11] D. Gabay. Minimizing a differentiable function over a differential manifold , 1982 .
[12] John E. Dennis,et al. Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.
[13] F. Chatelin. Simultaneous Newton’s Iteration for the Eigenproblem , 1984 .
[14] B. F. Doolin,et al. Introduction to Differential Geometry for Engineers , 1990 .
[15] W. Kendall. Probability, Convexity, and Harmonic Maps with Small Image I: Uniqueness and Fine Existence , 1990 .
[16] G. Golub,et al. Tracking a few extreme singular values and vectors in signal processing , 1990, Proc. IEEE.
[17] J.l. Ramos. Introduction to differential geometry for engineers , 1993 .
[18] J. Ferrer,et al. Differentiable families of subspaces , 1994 .
[19] C. Udriste,et al. Convex Functions and Optimization Methods on Riemannian Manifolds , 1994 .
[20] I. Chavel. Riemannian Geometry: Subject Index , 2006 .
[21] A. Bloch. Hamiltonian and Gradient Flows, Algorithms and Control , 1995 .
[22] Gene H. Golub,et al. Matrix computations (3rd ed.) , 1996 .
[23] Gene H. Golub,et al. Matrix Computations, Third Edition , 1996 .
[24] U. Helmke,et al. Optimization and Dynamical Systems , 1994, Proceedings of the IEEE.
[25] R. Mahony. The constrained newton method on a Lie group and the symmetric eigenvalue problem , 1996 .
[26] Alan Edelman,et al. The Geometry of Algorithms with Orthogonality Constraints , 1998, SIAM J. Matrix Anal. Appl..
[27] Eva Lundstr. Adaptive Eigenvalue Computations Using Newton's Method on the Grassmann Manifold , 1999 .
[28] Robert E. Mahony,et al. The Geometry of the Newton Method on Non-Compact Lie Groups , 2002, J. Glob. Optim..
[29] L. Eldén,et al. Inexact Rayleigh Quotient-Type Methods for Eigenvalue Computations , 2002 .
[30] L. Rodman,et al. A class of robustness problems in matrix analysis , 2002 .
[31] Robert E. Mahony,et al. A Grassmann-Rayleigh Quotient Iteration for Computing Invariant Subspaces , 2002, SIAM Rev..
[32] Roger P. Woods,et al. Characterizing volume and surface deformations in an atlas framework: theory, applications, and implementation , 2003, NeuroImage.
[33] Robert E. Mahony,et al. Cubically Convergent Iterations for Invariant Subspace Computation , 2004, SIAM J. Matrix Anal. Appl..
[34] James Demmel,et al. Three methods for refining estimates of invariant subspaces , 1987, Computing.