What is the purpose of the optional HxR regulators?

The HPR12/HNR12 are voltage regulators similar to the 7812/7912 ICs. The key differences are their wider bandwidth, lower noise, and lower output impedance. Additionally, they feature Kelvin-sense inputs, allowing the creation of a local regulator that does not need to be physically close to the circuit being powered. Typical op-amp based circuits exhibit significantly greater sensitivity to power supply ripple and noise than the DC PSRR values listed in the datasheet would indicate.