Marco Selig, Niels Oppermann, Torsten A. Enßlin
Estimating the diagonal entries of a matrix, that is not directly accessible
but only available as a linear operator in form of a computer routine, is a
common necessity in many computational applications, especially in image
reconstruction and statistical inference. Here, methods of statistical
inference itself are used to improve the accuracy or the computational costs of
matrix probing methods to estimate matrix diagonals. In particular, the
generalized Wiener filter methodology, as developed within information field
theory, is shown to significantly improve estimates based on only a few
sampling probes, in cases in which some form of continuity of the solution can
be assumed. The strength, length scale and precise functional form of the
exploited autocorrelation function of the matrix diagonal is determined from
the probes themselves. The developed algorithm is successfully applied to mock
and real world problems. These performance tests show that in situations, where
a matrix diagonal has to be calculated from only a small number of
computationally expensive probes, a speed-up by a factor of two to ten is
possible with the newly proposed method.
View original:
http://arxiv.org/abs/1108.0600
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