I am interested to see if there are any advantages to using purified
water in ironing. Please back up with as much factual information as
possible, with scientific and industry specific resources. Thanks.

Some irons require the use of distilled water, and some do not. For
best results, I suggest that you consult the user's manual of the iron
you are using, and follow the manufacturer's recommendation.

"Many people use distilled water in their irons for pressing clothes
to reduce mineral build-up and make the iron last longer. However,
many iron manufacturers say that distilled water is no longer
necessary in their irons, partly due to a perception that the water is
more likely to sputter into the user's face, and primarily because of
advanced materials that resist mineral build-up. For example, the
General Electric Walmart-branded model 'Type 163 Iron' (2005) includes
in its directions: Please do not use distilled water in this iron."

http://en.wikipedia.org/wiki/Distilled_water#Myths_about_distilled_water