Reddit reviews Power Acoustik PC1.5F 1.5 Farad Digital Power Capacitor

The 850w rating is likely peak output of the amp, meaning your math is correct for the max draw, but the average current will likely be much lower. Since the amp won't pass any DC component, the average current over a small window of time (longer than the period of the lowest frequency present in the signal) can't be more than half the peak current.

Also, it turns out computer power supplies are a great source of cheap 12V power. This might work: http://www.newegg.com/Product/Product.aspx?Item=N82E16817822013 It will give you 40A on the +12V rail. In order to handle the 86A peaks, you can add a big capacitor. Something like this: http://www.amazon.com/Power-Acoustik-PC1-5F-Digital-Capacitor/dp/B002YT84QM

I have an old car sub/amp at home that I run off a power supply I pulled from a pile of computers going to the trash. I don't have a cap on it and it works just fine.

A couple of notes on how to actually use a computer PSU: You will need all the black wires (ground) all the yellow wires (+12V) and the one green wire that is supposed to go to the motherboard. The green wire turns on the PSU when it is shorted to ground (one of the black wires). I opened up the case of mine and cut all the wires that I didn't need to keep things clean. I also added a switch between green and one of the ground wires to turn it on and off.

Good luck!