From BlenderWiki

Subdivide Smooth

The sample mesh (a cube).

Subdivide Smooth, with a factor of 1.0.

Subdivide Smooth (located in the Mesh » Edges or Specials menus) works exactly as Subdivide, except that all newly created vertices are translated to lower the sharpness of the mesh, so that the resulting mesh seems to have been Smoothed. A sort of raw, basic subsurf…

However, the smoothing is not exactly the same as with Smooth (e.g., it only works with angled faces – this is why we used a cube as example, instead of the plane “grid” used to illustrates the previous tools), and the smooth factor asked by the pop-up numeric field might be from 0.0 (no smoothing) to 5.0 (sort of “over smoothing” that makes things sharper…), 1.0 being the default and “smoother” value. Note that this tool is not represented in the Mesh Tools panel, even though it uses the same settings as the other Subdivide ones.

Unfortunately, there does not seem to be any “multi” version of this tool…