An alternative would be to buy a box that can convert analog to digital, with an HDMI output. These exist and are a couple hundred dollars or more. Lastly, you may be able to output from your standard VGA out, into the JVC’s component video, but that is likely to not work in most cases. (I didn’t try that).
As you can see, there are workarounds, but, geez, JVC had no business leaving that out. Shame! It’s not that the possible solutions are a lot of money – certainly compared to an over $5000 projector, it’s just the hassle for those with computers lacking HDMI output.
OK, I’m done with that rant. Moving right along, The JVC has two HDMI inputs compared to the Sharp’s two HDMI inputs and a third digital, DVI (HDMI compatible input). The Sharp offers two component video inputs, to the JVC’s one, however they both have not just the R,G,B connectors, but two more (each) for syncing with a wider array of devices, and, for example can be used for a typical analog computer input, which is exactly how Sharp would handle a typical computer. It’s just a matter of the right cable.