KNOTWEED? not sure what it is, but if you're worried about surrounding vegetation, you'll need to pour a killing agent directly into the ground at the base of the plant.
MY thrifty home remedy for ANY unwanted growth is White vinegar. I apply over & over (usually 2-4 times) until it gets to the root & kills once & for all!
You can also use diesel fuel or probably straight gasoline for that matter. However, considering the price of gas lately ($2.65/gallon in my neck of the woods Central Virginia as of 10/25/07) it would probably be just as cheap to buy ROUNDUP & spray it on.