Simple, basic and works MOST of the time.
...but not ALL of the time.
The 79xx are known for latchup if the +Ve rail wakes up first, which happens some of the time with this non-center-tapped-secondary approach.
I prefer the center-tapped version.
Alternative quick-fix is to put a diode in the ground-sensing leg of each regulator, to raise the output by a diode-drop (about 0.6V) and compensate for the other two diode which you stick inseries with the +VE and -VE outputs respectively... one in each.
Keith