Paper Info
Title
Fast methods for estimating the Numerical rank of large matrices.
Abstract
We present two computationally inexpensive techniques for estimating the numerical rank of a matrix, combining powerful tools from computational linear algebra. These techniques exploit three key ingredients. The first is to approximate the projector on the non-null invariant subspace of the matrix by using a polynomial filter. Two types of filters are discussed, one based on Hermite interpolation and the other based on Chebyshev expansions. The second ingredient employs stochastic trace estimators to compute the rank of this wanted eigen-projector, which yields the desired rank of the matrix. In order to obtain a good filter, it is necessary to detect a gap between the eigenvalues that correspond to noise and the relevant eigenvalues that correspond to the nonnull invariant subspace. The third ingredient of the proposed approaches exploits the idea of spectral density, popular in physics, and the Lanczos spectroscopic method to locate this gap.
Year
Venue
Field
2016
ICML
Rank (linear algebra),Applied mathematics,Linear algebra,Lanczos resampling,Polynomial,Computer science,Matrix (mathematics),Invariant subspace,Artificial intelligence,Hermite interpolation,Eigenvalues and eigenvectors,Discrete mathematics,Pattern recognition
DocType
Citations 
PageRank 
Conference
11
0.56
References 
Authors
14
2
Name
Order
Citations
PageRank
shashanka ubaru1588.97
Yousef Saad21940254.74