The inertia of an n × n matrix A is defined as the triple (i+(A), i−(A), i0(A)), where i+(A), i−(A), and i0(A) are the number of eigenvalues of A, counting multiplicities, w...
We shall give simpler proofs of some lower bounds on monotone computations. We describe a simple condition on combinatorial structures, such that the rank of the matrix associated...
We describe some major recent progress in exact and symbolic linear algebra. These advances concern the improvement of complexity estimates for fundamental problems such as linear...
Resultants characterize the existence of roots of systems of multivariate nonlinear polynomial equations, while their matrices reduce the computation of all common zeros to a prob...
Point-based algorithms have been surprisingly successful in computing approximately optimal solutions for partially observable Markov decision processes (POMDPs) in high dimension...