Randomized methods for rank-deficient linear systems
Numerical Analysis
2014-01-15 v1
Abstract
We present a simple, accurate method for solving consistent, rank-deficient linear systems, with or without addi- tional rank-completing constraints. Such problems arise in a variety of applications, such as the computation of the eigenvectors of a matrix corresponding to a known eigenvalue. The method is based on elementary linear algebra combined with the ob- servation that if the matrix is rank-k deficient, then a random rank-k perturbation yields a nonsingular matrix with probability 1.
Cite
@article{arxiv.1401.3068,
title = {Randomized methods for rank-deficient linear systems},
author = {Josef Sifuentes and Zydrunas Gimbutas and Leslie Greengard},
journal= {arXiv preprint arXiv:1401.3068},
year = {2014}
}