I am currently working on a research project that is trying to show that some numerical integration techniques that do well on separable convex functions will not necessarily do well on non-separable convex functions. I hope to show this using by testing these numerical integration techniques on functions of the form:
$f: \mathbb{R}^n \rightarrow \mathbb{R}$ where $f(x) = x^T Q x$
For the purposes of my test, I need $f$ to be convex and relatively "general" (in the sense that the entries of $Q$ are relatively variety and my function $f$ does not look 'special' in some kind of way). Does anyone know of a nice way to generate an $n \times n$ matrix $Q$ that will yield a convex function $f$?