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A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its L_infinity-norm
Matrix and singular value differentiable function frequency singular value lipschitz second derivative
2015/8/12
The ith singular value of a transfer matrix need not be a differentiable function of frequency where its multiplicity is greater than one. We show that near a local maximum, however, the largest singu...
Low-Rank Matrix Approximation with Weights or Missing Data is NP-hard
low-rank matrix approximation weighted low-rank approximation missing data
2011/1/17
Weighted low-rank approximation (WLRA), a dimensionality reduction technique for data anal-
ysis, has been successfully used in several applications, such as in collaborative filtering to design reco...
We continue the analysis in [F. Hansen, and J. Tomiyama, Differential analysis of matrix convex functions. Linear Algebra Appl., 420:102--116, 2007] of matrix convex functions of a fixed order defined...