We design a new distribution over m× n matrices S so that, for any fixed n× d matrix A of rank
r, with probability at least 9/10,∥ SAx∥ 2=(1±ε)∥ Ax∥ 2 simultaneously for all x∈ R d …

An oblivious subspace embedding (OSE) given some parameters ε, d is a distribution D over
matrices Π∈ R m× n such that for any linear subspace W⊆ R n with dim (W)= d, P Π~ D (∀ …

The dynamic matrix inverse problem is to maintain the inverse of a matrix undergoing
element and column updates. It is the main subroutine behind the best algorithms for many …

We present a general framework of designing efficient dynamic approximate algorithms for
optimization problems on undirected graphs. In particular, we develop a technique that …

Even after decades of quantum computing development, examples of generally useful
quantum algorithms with exponential speedups over classical counterparts are scarce …

We create classical (non-quantum) dynamic data structures supporting queries for
recommender systems and least-squares regression that are comparable to their quantum …

We study fundamental problems in linear algebra, such as finding a maximal linearly
independent subset of rows or columns (a basis), solving linear regression, or computing a …

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Matrices with low-rank structure are ubiquitous in scientific computing. Choosing an
appropriate rank is a key step in many computational algorithms that exploit low-rank …

We show that any nonzero polynomial in the ideal generated by the r× r minors of an n× n
matrix X can be used to efficiently approximate the determinant. Specifically, for any nonzero …