The Beylkin-Cramer summation rule and a new fast algorithm of cosmic statistics for large data sets

	The Beylkin-Cramer summation rule and a new fast algorithm of cosmic statistics for large data sets
	Feng, Long-Long
刊名	ASTROPHYSICAL JOURNAL
	2007-03-20
卷号	658 期号:1 页码:25-35
关键词	large-scale structure of universe
英文摘要	Based on the Beylkin- Cramer summation rule, we introduce a new fast algorithm that enables us to explore the high- order statistics efficiently in large data sets. Central to this technique is to make decompositions both of fields and operators within the framework of multiresolution analysis and to realize their discrete representations. Accordingly, a homogeneous point process could be equivalently described by the operation of a Toeplitz matrix on a vector, which is accomplished bymaking use of the fast Fourier transformation. The algorithm could be applied widely in cosmic statistics to tackle large data sets. We demonstrate this novel technique using the spherical, cubic, and cylindrical counts in cells. The numerical test shows that the algorithm produces an excellent agreement with the expected results. Moreover, the algorithm naturally introduces a sharp filter, which is capable of suppressing shot noise in weak signals. In the numerical procedures, the algorithm is somewhat similar to particle- meshmethods in N- body simulations. Since it is scaled with O( N log N), it is significantly faster than the current particle- based methods, and its computational cost does not rely on the shape or size of the sampling cells. In addition, based on this technique, we further propose a simple fast scheme to compute the second statistics for cosmic density fields and justify it using simulation samples. Hopefully, the technique developed here allows us to make a comprehensive study of nonGaussianity of the cosmic fields in high- precision cosmology. A specific implementation of the algorithm is publicly available on request to the author.
WOS标题词	Science & Technology ; Physical Sciences
类目[WOS]	Astronomy & Astrophysics
研究领域[WOS]	Astronomy & Astrophysics
关键词[WOS]	GALAXY REDSHIFT SURVEY ; 3-POINT CORRELATION-FUNCTION ; POWER SPECTRUM ; HALO MODEL ; EVOLUTION ; UNIVERSE ; FIELD ; BIAS
收录类别	SCI
语种	英语
WOS记录号	WOS:000244928900003
内容类型	期刊论文
源URL	[http://libir.pmo.ac.cn/handle/332002/15852]
专题	紫金山天文台_南极天文中心
作者单位	1.Acad Sinica, Purple Mt Observ, Nanjing 210008, Peoples R China 2.Joint Ctr Particle Nucl Phys & Cosmol, Nanjing, Peoples R China
推荐引用方式 GB/T 7714	Feng, Long-Long. The Beylkin-Cramer summation rule and a new fast algorithm of cosmic statistics for large data sets[J]. ASTROPHYSICAL JOURNAL,2007,658(1):25-35.
APA	Feng, Long-Long.(2007).The Beylkin-Cramer summation rule and a new fast algorithm of cosmic statistics for large data sets.ASTROPHYSICAL JOURNAL,658(1),25-35.
MLA	Feng, Long-Long."The Beylkin-Cramer summation rule and a new fast algorithm of cosmic statistics for large data sets".ASTROPHYSICAL JOURNAL 658.1(2007):25-35.