The answer to this question (Volatility surface interpolation for Black-Scholes delta hedging) names Cubic Spline Interpolation and Guassian Process interpolation (is this exactly the same thing as Kriging?). What are the pros and cons of each method and are there different methods to consider than these two (apart from simple linear interpolation)?
Further, what are some good references for each method, are there any special considerations that should be taken when applying the methods to volatility surfaces specifically? Specifically for Gaussian Process interpolation as that seems to be far more complicated.