On Symmetric Factorizations of Hankel Matrices

We present two conjectures regarding the running time of computing symmetric factorizations for a Hankel matrix H and its inverse H-1 as BB* under fixed-point arithmetic. If solved, these would result in a faster-than-matrix-multiplication algorithm for solving sparse poly-conditioned linear programming problems, a fundamental problem in optimization and theoretical computer science. To justify our proposed conjectures and running times, we show weaker results of computing decompositions of the form BB* - CC* for Hankel matrices and their inverses with the same running time.