2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) (2017)
Berkeley, California, USA
Oct. 15, 2017 to Oct. 17, 2017
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/FOCS.2017.69
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 we will develop nearly-linear time algorithms for solving all systems of linear equations over the reals, or progress on the families we can solve in nearly-linear time will soon halt.
computational complexity, eigenvalues and eigenfunctions, linear systems, matrix algebra
R. Kyng and P. Zhang, "Hardness Results for Structured Linear Systems," 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), Berkeley, California, USA, 2017, pp. 684-695.