I haven't found any good information on this topic. What I can tell you is from my experience with my Galaxy Nexus. (I found this post through a Google search on the topic.)
I can do HDMI out through the MHL adapter with no issues. However, once I plug in an HDMI to DVI converter, and then out to either a standard or widescreen Dell monitor, the display blanks out unless there is some motion taking place on the screen. The motion I am talking about is either touching the screen and moving between homescreens, or playing a flash video/netflix video. Yet, even when the display is working with some type of motion, there is a terrible flicker that shows on the screen.
No luck yet remedying this... and not enough knowledge about the conversion between HDMI and DVI and why the monitor may be seeing no signal. I am assuming the HDMI cables transmits an idle signal in a certain manner that doesn't make it through the DVI changeover.
Hopefully someone can shed some light on this!
TL;DR - HDMI to DVI conversion doesn't work well on Galaxy Nexus, either.