On factor width and symmetric H-matrices

We define a matrix concept we call factor width. This gives a hierarchy of matrix classes for symmetric positive semidefinite matrices, or a set of nested cones. We prove that the set of symmetric matrices with factor width at most two is exactly the class of (possibly singular) symmetric H-matrices (also known as generalized diagonally dominant matrices) with positive diagonals, H+. We prove bounds on the factor width, including one that is tight for factor widths up to two, and pose several open questions.