The 100K resistors are FAR too high to generate a split supply, unless you are drawing exactly the same current from the positive and negative rails.
If you want to generate a split supply in this way I would suggest you use an opamp to generate the spit supply - it's a common technique, there are examples everywhere, and it's often used in commercial equipment as well.
If an opamp won't provide enough current to balance the two rails, you can add extra output transistors to increase it's current handling - again, a common technique!.
But probably easier, how about buying two cheap switch-mode regulated wallwart type supplies?, set them both to 9V, and use one for each rail?. Ones I have here are rated at 1A current.