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[[File:Extended_Sparse_Matrix.png|thumb|Extended Sparse Matrix arising from a <math>10 \times 10</math> semi-separable matrix whose semi-separable rank is <math>4</math>.]]
The '''Rybicki–Press algorithm''' is a fast direct [[algorithm]] for inverting a [[Matrix (mathematics)|matrix]], whose entries are given by <math>A(i,j) = \exp(-a \vert t_i - t_j \vert)</math>, where <math>a \in \mathbb{R}</math>.<ref>{{citation
|last1 = Rybicki|first1 = George B.|last2 = Press|first2 = William H.|arxiv = comp-gas/9405004|doi = 10.1103/PhysRevLett.74.1060|journal = Physical Review Letters|title = Class of fast methods for processing Irregularly sampled or otherwise inhomogeneous one-dimensional data|volume = 74|issue = 7|pages = 1060–1063|year = 1995|bibcode = 1995PhRvL..74.1060R|pmid=10058924}} {{Open access}}</ref> It is a computational optimization of a general set of statistical methods developed to determine whether two noisy, irregularly sampled data sets are, in fact, dimensionally shifted representations of the same underlying function.<ref>{{Cite journal|title = Interpolation, realization, and reconstruction of noisy, irregularly sampled data|last = Rybicki|first = George B.|date = October 1992|journal = The Astrophysical Journal|doi = 10.1086/171845|last2 = Press|first2 = William H.|bibcode = 1992ApJ...398..169R|volume=398|page=169}}{{Open access}}</ref><ref name=":0">{{Cite journal|last=MacLeod|first=C. L.|last2=Brooks|first2=K.|last3=Ivezic|first3=Z.|last4=Kochanek|first4=C. S.|last5=Gibson|first5=R.|last6=Meisner|first6=A.|last7=Kozlowski|first7=S.|last8=Sesar|first8=B.|last9=Becker|first9=A. C.|date=2011-02-10|title=Quasar Selection Based on Photometric Variability|journal=The Astrophysical Journal|volume=728|issue=1|pages=26|doi=10.1088/0004-637X/728/1/26|issn=0004-637X|arxiv=1009.2081|bibcode=2011ApJ...728...26M}}</ref> The most common use of the algorithm is in the detection of periodicity in astronomical observations.<ref name=":0" />
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