My research interests include randomized numerical linear algebra, parameter identifiability, and mathematical modeling. Here's my CV. Here's my Google Scholar page with the most up-to-date publication list.
My postdoctoral research at the Oden Institute with Gunnar Martinsson's group centers on randomized algorithms for low-rank matrix and tensor approximation.
This paper develops an adaptive randomized algorithm to determine approximate interpolative decompositions of large matrices using LU with partial pivoting (LUPP). Deterministic algorithms for LUPP are notoriously not rank-revealing (e.g. Wilkinson (1965), Kahan (1965), Golub (1965)), whereas deterministic QR with column pivoting (QRCP) rarely fails to be rank-revealing in practice. Both randomized and deterministic versions of QRCP are also easy to make adaptive (i.e. with a prescribed tolerance for the residual approximation error) because of the orthonormal basis computations involved. However, as a result, QRCP is more computationally expensive than LUPP and more difficult to parallelize for high-performance computing.
This paper also develops an adaptive randomized algorithm, based on blockwise random pivoting.
This paper develops randomized algorithms for rank-structured matrices. A rank-structured matrix is one which can be tessellated into a number of submatrices, or blocks, which are either small enough to work with directly or else are well-approximated by a low-rank matrix. Finding the representation of the input matrix in terms of these low-rank factors is known as compression. Rank-structured matrix compression is relevant to many scientific applications, such as machine learning (kernel matrices) or fast direct solvers for elliptic PDEs (dense Schur complements in LU factorizations of sparse matrices). However, because of the huge problem sizes associated with many of these applications, deterministic algorithms to compute the low-rank basis matrices for admissible blocks are intractable due to issues like memory inefficiency and computational costs.
This paper is an in-depth survey of recent advances in randomized algorithms for low-rank matrix and tensor decompositions.
This paper presents column subset selection algorithms in the context of parameter identifiability for mathematical modeling applications.
This paper develops a mathematical model for a wound healing application.