Error analysis for stellar population synthesis as an inverse problem

Stellar population synthesis can be approached as an inverse problem. The physical information is extracted from the observations through an inverse model. The process requires the transformation of the observational errors into model errors. A description is given for the error analysis to obtain objectively the errors in the model. Finding a solution for overdetermined and under-determined case was the purpose of two preceding papers. This new one completes the problem of stellar populations synthesis by means of a data base, by providing practical formul\ae defining the set of acceptable solutions. All solutions within this set are compatible, at a given confidence level, with the observations.