Rybicki Press algorithm

The Rybicki–Press algorithm is a fast direct algorithm for inverting a matrix, whose entries are given by $A(i,j)=\exp(-a\vert t_{i}-t_{j}\vert )$ , where $a\in \mathbb {R}$ .^[1] 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.^[2]^[3]^: 2 The most common use of the algorithm as of 2015 is in the detection of periodicity in astronomical observations.^{[citation needed]}

References

^ Rybicki, George B.; Press, William H. (1995), "Class of fast methods for processing Irregularly sampled or otherwise inhomogeneous one-dimensional data", Physical Review Letters, 74: 1060, arXiv:comp-gas/9405004, Bibcode:1995PhRvL..74.1060R, doi:10.1103/PhysRevLett.74.1060
^ Rybicki, George B.; Press, William H. (October 1992). "Interpolation, realization, and reconstruction of noisy, irregularly sampled data". The Astrophysical Journal. Bibcode:1992ApJ...398..169R. doi:10.1086/171845.
^ McLeod, C. L.; et al. (February 2011). "Quasar Selection Based on Photometric Variability". The Astrophysical Journal. arXiv:1009.2081. Bibcode:2011ApJ...728...26M. doi:10.1088/0004-637X/728/1/26.

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[1] Rybicki, George B.; Press, William H. (1995), "Class of fast methods for processing Irregularly sampled or otherwise inhomogeneous one-dimensional data", Physical Review Letters, 74: 1060, arXiv:comp-gas/9405004, Bibcode:1995PhRvL..74.1060R, doi:10.1103/PhysRevLett.74.1060

[2] Rybicki, George B.; Press, William H. (October 1992). "Interpolation, realization, and reconstruction of noisy, irregularly sampled data". The Astrophysical Journal. Bibcode:1992ApJ...398..169R. doi:10.1086/171845.

[3] McLeod, C. L.; et al. (February 2011). "Quasar Selection Based on Photometric Variability". The Astrophysical Journal. arXiv:1009.2081. Bibcode:2011ApJ...728...26M. doi:10.1088/0004-637X/728/1/26.

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