A new inverse method for stellar population synthesis and error analysis.

International audienceThe stellar population synthesis in unresolved composite objects is a very tricky problem. Indeed, it is a degenerate problem since many parameters affect the observables. The stellar population synthesis issue thus deserves a deep and rigourous analysis. In this paper we present a method of inversion which uses as observables the intensities at each pixel of a galactic spectrum and provides the stellar contribution to luminosity of all stars considered in a database. The main contribution of this paper to the synthesis problem is that it provides an analytical computation of the uncertainties accompanying a solution. This constitutes an important improvement relative to previous methods which do not provide such infomation except in the method described by Pelat (\cite{Pelat97}) and Moultaka & Pelat (\cite{Moultaka00}). The latter uses the equivalent widths and intensities of stellar spectra in order to reproduce the equivalent widths of a galactic spectrum. The novelty of this work relative to the previous one is that the dust emission present in the IR spectra can be modeled as well as the velocity dispersion of stars that broadens the lines of a galactic spectrum. Tests are also performed in order to estimate the reliability of the method and the influence on the results of an additive continuum present in a studied spectrum, for example in the case of AGNs