The Example schematic only has 100uF + 0.1uF + 1000pF across the rails.
Have you considered the "mF" may be a typo? In one place, the datasheet says typically 0.1 mF to 1 uF. I wonder if they meant to type n, and accidentally hit m. Also, I copied the u symbol out of the PDF, and it got printed as m when it was pasted. Cut&Paste may be at fault here, it certainly seems to be used within TI's various datasheets.
Also, millifarads have come to be an almost unused unit. It's generally Farads -> microFarads -> (nanoFarads - somewhat uncommon) -> picoFarads.
Furthermore, looking at the TPA3111 Evaluation Kit is informative:
The device is bypassed with two 100uF electrolytics (along with 0.1uF and 1000pF ceramics).
Also, looking at similar parts from the same line is informative. The TPA3110 (15W vs TPA3111's 10W) merely says a larger aluminum electrolytic capacitor of 220 uF or greater placed near the audio power amplifier is recommended. It's worth noting that the same datasheet's example schematics only use two 100uF caps for bypassing.
The same note as in the TPA3111 is present in the TPA3112 datasheet.
It's also worth noting that the TPA3110 and TPA3113 have identical "Power Supply Decoupling" paragraphs, despite the fact that one is half the power of the other (15W vs 6W), which further inclines me to think typo.
The 25W TPA3123 only recommends 470uF of bulk capacitance.
The 100W TAS5121 only recommends 1000uF.
Edit: We will see if it is a typo: "Below is what you submitted to tis-doc-errors@list.ti.com on Tuesday, July 26, 2011 at 04:13:23; E-mail: tis-doc-errors@list.ti.com Lit Number: SLOS618BB Part Number: TPA3111D1 Error Page No: 19 Error Description: Please see this thread: HUGE capacitor recommended in datasheet for Audio Amp"
looking at the datasheet, your dc power supply is not sufficient.
I would size it about twice the non repetitive peak Amperage for power headroom, but twice its repetitive peak output would be my recommended minimum.
If you go by typical practices, the maximum current draw should be 80% of the power supply so the rectifier filters in the power supply can recover.
But that is only the 1/3 of the issue, the main issue it has is its design.
Unbalanced = 100% of power supply noise injected onto the signal.
Now if you create isolated power, or create a ground reference that has the inverse of the power supply noise on the ground, the noise would get subtracted by the output circuit.
Best Answer
Let's say the load of the AUDIO POWER is around 4 ohms. And the requirement is to have the power rail changes no more than 5% with 100% changing 4 ohm load, therefore the power supply impedance needs to be less then 4 ohm x 5% = 0.2 ohm.
Further assume that the power supply is an unknown cannot be relied on and the 0.2 ohm impedance is to be satisfied with on-board capacitors only at 40Hz (lowest audio frequency desired).
C = 1 / (2 * pi * freq * 0.2) = 0.02 F = 20000 uF (I could be off by a factor of 2)
So at first glance, the capacitors seem way overkill, but there are conditions where they can be justified. It really depends on the load, the power supply and the requirements.