There are a lot of solutions out there for generating split +/-15V from a single DC voltage, but all are lacking in some way or another. Either their power levels are too high, they don't offer isolation, or they are exceedingly complex.
There is a part from TI that is incredibly versatile and designed for generating a range of supply outputs: It's the SN6501 and its higher power cousin the SN6505. Both of these parts are conceptually simple: They aim to drive the primary side of a center-tapped transformer in a push-pull fashion. These are open loop, meaning they blindly do what they need to do and as a result they don't have regulated outputs. But that's easy to fix.
The better part is that once you understand how they work, you can replace the parts with a simple drive circuit from an FPGA in certain application.
We use the SN6501 a lot in our designs with isolation. The QA401 has 4 of them to generate the +/- rails and also the isolated 5V and 3.3V. This means 4 transformers, but the transformers are fairly modest in size for our applications: about 10x10 mm. But with a little work, you could replace the 4 transformers with 2 and still get a 4 isolated supplies. The experiment below is a stop on that path.
Test Circuit
The test circuit below is derived from Figure 48 in the SN6501 spec. 
Working from the left, we see a USB input, followed by the ability to dual-place an SN6501 or an SN6505 on the same footprint. The SN6505 offers about 3X higher drive capability if needed. The transformer is a Wurth 760390013. This is followed by a half-wave rectifier, some filter caps, and two LDOs: One for the positive rail and another for the negative rail. The positive rail LDO is a TPS7A49, which is a 150 mA "ultra-low noise" regulator. The negative rail is a TPS7A30 200mA "ultra low-noise" regulator.
To put the low-noise claims into context, both specs are indicating around 15 uV of noise in the 20 to 20 KHz bandwidth. A plot of the positive rail regulator output noise from the spec is shown below:
From the above, we see the 15 uV noise figure is achieved at 1.2V output, but that the noise rises quickly below 100 Hz as the output voltage increases. The spec didn't have a lot of detail as to what their might mean for 15V operation, but assume it's worse given the 1.2V to 5V trend.
The Measurements
The first measurement is a no-load measurement with the test circuit powered from a USB hub. Here we see the measured noise (20 to 20K) is 52.9 uV, which is reasonable (for comparison, the noise floor of the QA401 from 20 to 20K with inputs shorted is about 1.8uV. In other words, the QA401 could easily measure the noise in a circuit 10X less noisy.) Before you make a DC measurement on your QA401, make sure you have read the manual. DC measurements below +/-5V in magnitude are readily made. But beyond those limits, you must consider peak currents involved. See the manual for a discussion on this, as well as the tradeoffs to be made. Ignoring these cautions can damage your QA401. And never, ever, make measurements of voltages that are potentially hazardous or lethal with your QA401.
Adding a resistive load to the positive rail output raises the noise slightly. Below, a 20 mA load (680 ohm resistor) is added the outputs and overlaid with the original measurement. A slight increase to the noise floor can be seen. At this load, the input to the linear regulator is about 16.15V. This is a 16.15 (Vin) - 14.8V (Vout) = 1.35V drop, which is well above the typical regulator dropout voltage of 260mV @ 100 mA. Ideally, we'd probably want a 1.6 or 1.5:1 transformer, but that isn't an option.
Finally, we can look the loaded circuit in a wider bandwidth of 10 Hz to 90 KHz and we see the noise is reported at 62uV.
This wider bandwidth is interesting for two reasons. First, we can see the broader spectral content and we can readily see there is a spur at 25 KHz at -100 dBV (about 10 uV RMS). Second, the LM7815 typically has noise around 90 uV in this bandwidth. And the LM7815 has powered a lot of audio circuits over the years and will continue to power a lot of circuits due to its phenomenal cost. It's nice to have something that deliver a big improvement over the 7815, although as we'll see below, it might not be worth the cost.
What it means
A modern op-amp will give us at least 50 dB of rejection on any power supply noise. For example, the OPA1612 will deliver about 60 dB of PSRR across the audio band. As a first-order approximation: If our power supply noise is 60 uVrms, and that is hammered down 50-60 dB by the PSRR of the op-amp, then than means the input referenced noise into the op-amp will be about 100 nVrms . An op-amp like the OPA1612 has an input noise voltage of 1.2uVpp, so we're fine in that regard. That is, the noise contribution of from the power supply will be about 1/10th that of the opamp itself. Heck, even the LM7815 would do fine here.
But studying the curves a bit more indicates the situation gets better. A lot better. Note that the regulator output noise is higher at lower frequencies. But the PSRR of the op-amp is better at lower frequencies too. Relative to 1 KHz, the regulator noise rises about 15 dB at 100 Hz. But the PSRR improves about 20 dB. So in general, the fact that the noise of regulator increases at lower frequencies is more than addressed by the fact that the PSRR improves at lower frequencies. And that 10 uV spur we saw at 22 KHz would get hammered down to -170 dBV
In other words, this supply could readily provide the power for a modern op-amp like the OPA1612 and not impact the specs of that op-amp in the least.
Cost Consideration
The TPS7A49 regulator, and its negative rail counterpart (the TPS7A30), aren't cheap. Quantity 1 at Digikey for the pair would run you over $6. A 7815 and 7915 in DPAK package would run about $1.5. Is it worth it? More study would be needed, but based on the above, whether you were running an OPA1612 from a newer solutions or older solutions, there likely wouldn't be a measurable difference.
The drive from the SN6501 is easy to replicate in an FGPA. A CPU would have problems, because an error in drive symmetry will result in the transformer becoming saturated and operation failing catastrophically. If you are going to drive from a FPGA, study the Rds(on) of the MOSFETs you use. Normally, you'd pick something with a low Rds(on), but there's value in picking something with a higher Rds(on) because you want the MOSFET to heat if the drive currents start to become imbalanced. The higher Rds(on) will cause the MOSFET temp to climb as its asked to handle more current, and that will in turn limit the "on" current. It's another hit on efficiency, for sure. But remember, this family of circuits isn't picked for efficiency. It's picked for cost and performance.
Summary
A simple circuit was shown that delivers solid performance in a compact space with minimal part count and cost. The outputs are fully isolated (1KV or more if you desire) from the input and the circuit delivers noise performance that won't degrade the stellar noise performance of a top-end op-amp today.
The circuit can deliver about +/- 50 mA at +/-15V. Efficiency is not great at 72%, but that is a reasonable trade-off given the other wins.
Add a comment if you know a cheaper/simpler/better way to generate an isolated +/-15V split rail good for ~2W. We'd love to know the solution.