Fast n-point correlation functions and three-point lensing application

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dc.creatorZhang, Lucy Liuxuan
dc.creatorPen, Ue-Li
dc.date2003-05-23
dc.date2005-04-29
dc.date.accessioned2026-07-07T02:08:34Z
dc.date.available2026-07-07T02:08:34Z
dc.descriptionWe present a new algorithm to rapidly compute the two-point (2PCF), three-point (3PCF) and n-point (n-PCF) correlation functions in roughly O(N log N) time for N particles, instead of O(N^n) as required by brute force approaches. The algorithm enables an estimate of the full 3PCF for as many as 10^6 galaxies. This technique exploits node-to-node correlations of a recursive bisectional binary tree. A balanced tree construction minimizes the depth of the tree and the worst case error at each node. The algorithm presented in this paper can be applied to problems with arbitrary geometry. We describe the detailed implementation to compute the two point function and all eight components of the 3PCF for a two-component field, with attention to shear fields generated by gravitational lensing. We also generalize the algorithm to compute the n-point correlation function for a scalar field in k dimensions where n and k are arbitrary positive integers.
dc.description37 pages, 6 figures, LaTeX; added and modified figures, modified theoretical estimate of computing time; accepted by New Astronomy
dc.identifierhttps://arxiv.org/abs/astro-ph/0305447
dc.identifierhttp://arxiv.org/abs/astro-ph/0305447
dc.identifierNew Astron. 10 (2005) 569-590
dc.identifierdoi:10.1016/j.newast.2005.04.002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/6102
dc.subjectAstrophysics
dc.subjectComputational Complexity
dc.subjectData Structures and Algorithms
dc.titleFast n-point correlation functions and three-point lensing application
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