Topics in matrix analysis
Relative perturbation techniques for singular value problems
SIAM Journal on Numerical Analysis
Perturbation Analysis For Two-Sided (or Complete) Orthogonal Decompositions
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Semidefinite Programs: New Search Directions, Smoothing-Type Methods, and Numerical Results
SIAM Journal on Optimization
Fast Spectral Clustering with Random Projection and Sampling
MLDM '09 Proceedings of the 6th International Conference on Machine Learning and Data Mining in Pattern Recognition
Semi adaptive appearance models for lip tracking
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
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The spectral decomposition of a symmetric matrix A with small off-diagonal and distinct diagonal elements can be approximated using a direct scheme of R. Davies and Modi (Linear Algebra Appl. 77 (1986) 61). In this paper a generalization of this method for computing the singular value decomposition of close-to-diagonal A ∈ Rm×n is presented. When A has repeated or "close" singular values it is possible to apply the direct method to split the problem in two with one part containing the well-separated singular values and one requiring the computation of the "close" singular values.