Volume 44, pp. 177-188, 2015.
Randomized methods for rank-deficient linear systems
Josef Sifuentes, Zydrunas Gimbutas, and Leslie Greengard
Abstract
We present a simple, accurate method for solving consistent, rank-deficient
linear systems, with or without additional 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 observation that if the matrix is rank-
Full Text (PDF) [272 KB], BibTeX
Key words
rank-deficient systems, null space, null vectors, eigenvectors, randomized algorithms, integral equations
AMS subject classifications
15A03, 15A12, 15A18, 65F15, 65F99