A gradient descent method for solving of one class of nonlinear multiparameter eigenvalue problems

In the real Hilbert space the nonlinear multiparameter spectral problem is put in accordance to the variation problem on zero minimum of some functional. The equivalence of spectral and variation problems is proved. On the base of gradient procedure the numerical algorithm of finding its eigenvalues and eigenvectors is proposed. The local convergence of this algorithm is proved. The practical application of the algorithm is illustrated on example of nonlinear two-parameter eigenvalue problem.