Podlevs’kyi B. M.
Ukr. Mat. Zh. - 2009. - 61, № 9. - pp. 1247-1256
We associate a multiparameter spectral problem in a real Euclidean space with a variational problem of finding a minimum of a certain functional. We establish the equivalence of the spectralproblem and the variational problem. On the basis of the gradient procedure, we propose a numerical algorithm for the determination of its eigenvalues and eigenvectors. The local convergence of the algorithm is proved.
Ukr. Mat. Zh. - 2003. - 55, № 9. - pp. 1218-1223
We propose a method for the factorization of algebraic polynomials with real or complex coefficients and construct a numerical algorithm, which, along with the factorization of a polynomial with multiple roots, solves the problem of the determination of multiplicities and the number of multiple roots of the polynomial.
Ukr. Mat. Zh. - 1984. - 36, № 5. - pp. 658–660