Is there ANY way to eradicate this WEED? ALL suggestions/remedies appreciated!!!
Where are these growing?
What kind of soil?
What kind of light?
Generally these are plants that grow best in shady, moist soil, correct the growing conditions and most often they will die out.
You have my complete sympathy! Fool I, added this to my garden many years ago. It over powered my other plants in a very short time and I spent a day pulling it out by hand. Over the next two years I would find a sprout every know and then sticking up and would immediately pull. The last two years have been drought here and I didn't find any. This spring was very wet and I found 1 sprout.
Hopefully you do not have an extensively large patch and can also pull out by hand. Sorry to say that it takes either sweat and work to remove or as kimmsr says above change the growing conditions.