Mathematical problems in creating large astronomical catalogsстатья
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Аннотация:The next stage after performing observations and their primary
reduction is to transform the set of observations into a catalog.
To this end, objects that are irrelevant for the catalog should be excluded
from observations and gross errors should be discarded.
To transform such a prepared data set into a high-precision catalog, we need
to identify and correct systematic errors. To this end, each object of the survey
should be observed several, preferably many, times. The problem formally
reduces to solving an overdetermined set of equations. However, in the case of
catalogs this system has a very specic form: it is extremely sparse, and the
sparseness of the equation system increases rapidly with the number of objects
in the catalog. Such equation systems require special methods for storing data
on disks and in RAM, and for the choice of the techniques for solving the
corresponding equation systems. Another specic feature of such systems is
their high \stiffness", which also increases with the catalog volume. Special
stable mathematical methods should be used in order not to lose precision
when solving such equation systems. We illustrate the problem by the example
of photometric star catalogs, although similar problems arise in the case of
positional, radial-velocity, and parallax catalogs.