About one gradient procedure of determination of the branching points of nonlinear integral equation arising in the theory of antenna synthesis

The problem of building a numerical algorithm for determination of branching points of one nonlinear integral operator, which arises in the theory of antennas synthesis according to the given amplitude radiation pattern, is considered. The basic difficulty consists in that the kernel of an integral operator nonlinearly depends on two parameters, which play role of the spectral ones. For such problems, except a special ease, the existing numerical algorithms are not applicable. For building an algorithm for solving such problems, the equivalent variational statement is used, the problem is reduced to a sequence of linear two-parameter eigenvalue problems with application of one gradient procedure for simultaneous evaluation of two spectral parameters being the branching points of an initial nonlinear integral operator.