Speaker
Description
In low rank approximations to kernel matrices, skeletons consist of subsets of rows and columns from which CUR, ID, and related approximations can be formed. We consider applications in which parameter-dependent families of matrices with numerical low rank structures appear, such as in parameter dependent partial differential equations. We develop new techniques for analyzing and constructing universal skeletons. A universal skeleton is a single skeleton useful for the entire family of matrices; it captures shared low rank structures across the group. We also supply a practical and memory-efficient algorithm for constructing and using universal skeletons via proxy-point methods. To make things sufficiently scary, we develop universal skeletons in the hierarchical setting, and then use them to develop new fast direct solvers for applications involving multifrequency Helmholtz and Lippmann Schwinger equations.