- Journal Article
We show that if the nearly linear time solvers for Laplacian matrices and their generalizations can be extended to solve just slightly larger families of linear systems, then they can be used to quickly solve all systems of linear equations over the reals. This result can be viewed either positively or negatively: either nearly linear time algorithms can be developed for solving all systems of linear equations over the reals, or progress on the families that can be solved in nearly linear time will soon halt. Show more
Journal / seriesSIAM Journal on Computing
Pages / Article No.
PublisherSociety for Industrial and Applied Mathematics
Subjectnumerical linear algebra; linear system solvers; Laplacian solvers; multicommodity flow problems; truss stiffness matrices; total variation matrices; complexity theory; fine-grained complexity
MoreShow all metadata