Fast n-point Correlation Function Approximation with Recursive Convolution for Scalar Fields

In astrophysics, n-point Correlation Function (n-PCF) is an important tool for computation and analysis, but its algorithmic complex has long been a notorious problem. In this paper we are going to propose two algorithms that are easy to be parallized to compute the n-PCF problem efficiently. The algorithms are based on the definition of recursive convolution for scalar fields (RCSF), and it can be computed using varous fast Fourier Transform (FFT) algorithms in literature. Compared to traditional ways of dealing with this problem, our method is most efficient, for that it can achieve results with point sets as large as 1 billion in less than 1 minute. Moreover, the algorithms are intrinsically appropriate to be used on parallel computing environments such as computer clusters, multi-CPU/GPU super-computers, MapReduce and etc. Better computing environments can deal with better accuracy and time requirements.