A guide to analytic extrapolations I A program for optimal extrapolation to interior points

In the scattering theory of elementary particles as well as in any other branch of physics in which the analyticity of some function of physical interest has been established, one is often faced with the practical question of continuing data given on parts of the cuts in an analytic way towards some interior points of the analyticity domain. In order to get sensible predictions, one has to 'stabilize' the output by means, for instance, of a boundedness condition, given on those parts of the cuts where the actual data is lacking (e.g. a Froissart bound). The program ANALYT processes the input data and the stabilizing condition in an optimal function-analytic way, yielding estimates of analytic continuations in any desired interior point. Data spread on different energy regions can be correlated to get information about the asymptotics, or to find zeros and poles of the scattering amplitude. (13 refs).