The method used and preferred by garden presenter Monty Don is a flame gun, apparently if you weaken the the part of the plant above ground it will also weaken the root.
The one I saw him use looked very industrial and not the type with a small gas cylinder that will go out with the slightest breeze!
I agree with woofgang and find a strimmer the most suitable tool for the job!
Be prepared to replace the cord regularley, as it will wear down fast!
I invested in a conversion kit for my strimmer which saves me fiddling about with a spool. I just cut lengths of about 8" and plug them into the head. I bought that about 5 years ago and it's saved me a lot of time, money well spent!