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In this paper a new method is presented to find the transfer function of thebroad-line region in active galactic nuclei. The subtractive optimallylocalized averages (SOLA) method is a modified version of the Backus-Gilbertmethod and is presented as an alternative to the more often usedmaximum-entropy method. The SOLA method has been developed for use inhelioseismology. It has been applied to the solar oscillation frequencysplitting data currently available to deduce the internal rotation rate of thesun. The original SOLA method is reformulated in the present paper to cope withthe slightly different problem of inverting time series. We use simulations totest the viability of the method and apply the SOLA method to the real data ofthe Seyfert-1 galaxy NGC 5548. We investigate the effects of measurement errorsand how the resolution of the TF critically depends upon both the sampling rateand the photometric accuracy of the data. A uuencoded compressed postscriptfile of the paper which includes the figures is available by anonymous ftp atftp://solaris.astro.uu.se/pub/articles/atmos/frank/PijWan.uueComment: 16 pages, plain TeX using Blackwell MN macro

Reverberation mapping of active galactic nuclei: The SOLA method for time-series inversion