The entire area where I live is infested with this weed. 3 years ago I felt despondent as my previous years weeding seemed to increase this beast into a multi-headed monster. I researched this and found this advice. It has worked, but I will always have a problem but one which now takes 15 minutes every month to work at.
Mix a sachet of super strength Glysophate in the recommended amount of water. Once it has dispersed, add wallpaper paste to make a thick paste. Wearing rubber gloves and using a paint brush, apply this mixture to any of the weed that is in full growth, that is, it looks like a large loose bottle brush. You need to make sure each piece is covered from soil up over. Once it is covered, I gently get the frond to stick together and loosely coil it around itself and lay it on the ground. Don't waste time and paste on any shoots that are coming up, it wont have the desired effect.
3 Years ago, the task was monumental, last year much less so and this year its a case of working on any that pops up - and their isn't much of it.
At the start of the season, I mixed up a small plastic tupperware about a 1 pint size of the mixture. I leave it in the potting shed. When I find any of the beast I nip down to the shed and get my "rescue remedy". It works. Even if it pours down with half an hour of pasting it stays put.