Appears to be common Bermuda grass,is it not growing in lawns nearby? It primarly spreads by rhizomes and stolons but also makes seed. Rather than going into details on eradication,I reccomend looking at a recent post by chickencoop titled "composting Bermuda"in this soil forum.

That looks nothing like any Bermuda Grass I have seen and I doubt it would be growing in Iowa anyway.
To solarize (sun sterilize) you would need to remove all the plants you want to grow from the area, wet it quite thoroughly, and then cover the area with two layers of clear plastic for anywhere for 6 to 12 weeks, depending on the sun. That will heat the top 2, maybe 3 inches of soil high enough to kill any seeds in that soil.
If there are any of those plants growing anywhere within probably a mile the birds may be bringing more seeds in which is what is most likely what is germinating and growing in that patch.
Take a plant, in a sealable plastic baggie, to your local office of your Iowa State Universities Cooperative Extension Office for identification and maybe better methods of control.

Here is a link that might be useful: Bermuda Grass images

Thanks for your response kimmsr. Perhaps I should have pointed out out the weed in question is the one I pulled and laid on the rock. I lived in AZ for 25+ years so I know it isn't bermuda (even if it did grow in IA). My weed is not a grass of any type. But it is spreading heaviest under the tree where it started. It has tiny roots that don't run very deep but are too extensive to remove by hand. Very frustrating.

Classic case of can't see the wildflowers for the weeds.
40 lashes on me for looking at the wrong plant and overlooking the obivious one size fits all response,"take it to the local ag extension office". Not sure if that's one mistake or two but it's the first I've made in my life. If the thin blade plant in the foreground is cultivated , will you please identify it and what features in picture set it apart from Bermuda so I might recconize it.