On one approach to finding the branching lines and bifurcation points of solutions of nonlinear integral equations whose kernels depend analytically on two spectral parameters

We consider iterative algorithms of finding the curves of eigenvalues and their bifurcation points of a nonlinear algebraic two-parameter spectral problem, which appears in the solution of the problem of synthesis of plane antenna arrays by a given amplitude directivity pattern. These algorithms are based on the numerical procedure of calculation of ordinary and partial derivatives of a matrix determinant and the algorithm of finding all eigenvalues in a given domain of change in the spectral parameters. We also present some results of numerical experiments.