The optimal choice of initial approximations to solutions of regularized equations in the theory of branching

In [1, 2], V. A. Trenogin and the author proposed a method for constructing regularizing equations (R.E.) for ill-posed problems in the theory of branching [3, 4]. Here we consider the problem of choosing initial approximations, that are optimal in a certain sense, to simple solutions of R.E. in a neighborhood of a branching point.