This paper introduces the hierarchical interpolative factorization for integral equations (HIF-
IE) associated with elliptic problems in two and three dimensions. This factorization takes the …

In this work, we develop a fast hierarchical solver for solving large, sparse least squares
problems. We build upon the algorithm, spaQR (sparsified QR Gnanasekaran and Darve in …

We consider the approximate computation of spectral projectors for symmetric banded
matrices. While this problem has received considerable attention, especially in the context of …

In this work, we develop a new fast algorithm, spaQR---sparsified QR---for solving large,
sparse linear systems. The key to our approach lies in using low-rank approximations to …

We present a fast algorithm for linear least squares problems governed by hierarchically
block separable (HBS) matrices. Such matrices are generally dense but data sparse and …

Hierarchical matrices are dense but data-sparse matrices that use low-rank factorizations of
suitable submatrices to reduce the storage and computational cost to linear-polylogarithmic …

The QR factorization of a matrix is a fundamental operation in linear algebra and it is widely
utilized in scientific simulations. Although the QR factorization requires a memory storage of …

The efficient and accurate QR decomposition for matrices with hierarchical low-rank
structures, such as HODLR and hierarchical matrices, has been challenging. Existing …

We present two new algorithms for Householder QR factorization of Block Low-Rank (BLR)
matrices: one that performs block-column-wise QR and another that is based on tiled QR …

This thesis is on the numerical computation of eigenvalues of symmetric hierarchical
matrices. The numerical algorithms used for this computation are derivations of the LR …