We consider the problem of maintaining information about the rank of a matrix M under changes to its entries. For an n × n matrix M, we show an amortized upper bound of O(nω−1)...
This paper presents a Newton-like algorithm for solving systems of rank constrained linear matrix inequalities. Though local quadratic convergence of the algorithm is not a priori...
Given a matrix A, it is often desirable to find a good approximation to A that has low rank. We introduce a simple technique for accelerating the computation of such approximation...
The nested dissection method developed by Lipton, Rose, and Tarjan is a seminal method for quickly performing Gaussian elimination of symmetric real positive definite matrices who...
We prove that any real matrix A contains a subset of at most 4k/ + 2k log(k + 1) rows whose span "contains" a matrix of rank at most k with error only (1 + ) times the er...