Aaron Sidford (Stanford University)
In this talk I will discuss how to recover spectral approximations to broad classes of structured matrices using only a polylogarithmic number of adaptive linear measurements to either the matrix or its inverse. Leveraging this result I will discuss how to achieve faster algorithms for solving a variety of linear algebraic problems including solving linear systems in the inverse of symmetric M-matrices (a generalization of Laplacian systems), solving linear systems that are constant spectral approximations of Laplacians (or more generally, SDD matrices), and recovering a spectral sparsifier of a graph using only a polylogarithmc number of matrix vector multiplies. More broadly this talk will show how to leverage a number of recent approaches to spectral sparsification towards expanding the robustness and scope of recent nearly linear time linear system solving research, and providing general matrix recovery machinery that may serve as a stepping stone for faster algorithms. This talk reflects joint work with Arun Jambulapati and Kiran Shiragur.