does anybody know the source of any benchmark from where I can find data sets of positive-definite and dense (more than 50% non-zeros entry) matrices?
Why not simply generate them yourself? All you have to do is to generate a random(ish) rectangular matrix A and then create A.A', or a randomish rectangular matrix A and vector V and then create A.V.A'. You can vary the level of definiteness and so on easily.
I think benchmark matrices would be better for making out a publishable research paper that's why I was asking and I need them.