A Class of Fast Methods for Processing Irregularly Sampled or Otherwise Inhomogeneous One-Dimensional Data

Details A Class of Fast Methods for Processing Irregularly Sampled or Otherwise Inhomogeneous One-Dimensional Data A Class of Fast Methods for Processing Irregularly Sampled or Otherwise Inhomogeneous One-Dimensional Data

1994-05-20

arxiv.org/abs/comp-gas/9405004v1

Astronomy and Astrophysics

Astrophysics

7 pages, LaTeX with REVTeX 3.0 macros, no figures. A toolkit with implementations (in Fortran 90) of the algorithms is availab

Scientific paper

10.1103/PhysRevLett.74.1060

With the ansatz that a data set's correlation matrix has a certain parametrized form (one general enough, however, to allow the arbitrary specification of a slowly-varying decorrelation distance and population variance) the general machinery of Wiener or optimal filtering can be reduced from $O(n^3)$ to $O(n)$ operations, where $n$ is the size of the data set. The implied vast increases in computational speed can allow many common sub-optimal or heuristic data analysis methods to be replaced by fast, relatively sophisticated, statistical algorithms. Three examples are given: data rectification, high- or low- pass filtering, and linear least squares fitting to a model with unaligned data points.

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