Spectral condition‐number estimation of large sparse matrices
Abstract
We describe a randomized Krylov‐subspace method for estimating the spectral condition number of a real matrix A or indicating that it is numerically rank deficient. The main difficulty in estimating the condition number is the estimation of the smallest singular value of A. Our method estimates this value by solving a consistent linear least squares problem with a known solution using a specific Krylov‐subspace method called LSQR. In this method, the forward error tends to concentrate in the direction of a right singular vector corresponding to . Extensive experiments show that the method is able to estimate well the condition number of a wide array of matrices. It can sometimes estimate the condition number when running dense singular value decomposition would be impractical due to the computational cost or the memory requirements. The method uses very little memory (it inherits this property from LSQR), and it works equally well on square and rectangular matrices.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Mar 12, 2019
- Source ID
- 10.1002/nla.2235
Entities
People
- Alex Druinsky
- Haim Avron
- Sivan Toledo
Organizations
- Defense Advanced Research Projects Agency
- Israel Science Foundation
- Tel Aviv University