On a functional approach to constructing projections onto invariant subspaces of matrices (Q1288077)

A universal method is described for the approximate solution of a problem on trichotomy of a matrix spectrum with respect to the imaginary axis. The following is meant by universality of the method: The well-known matrix sign-function method and the method presented by the author [On construction of projections onto invariant subspaces of a matrix. Novosibirsk, Sobolev Institute of Mathematics, preprint No. 17 (1994)] which is based on solving a boundary value problem for a system of differential equations can be deduced from the described method. Besides the problem under consideration, the method can be used for solving a problem of dichotomy of a matrix spectrum and a problem of trichotomy of a matrix spectrum with respect to a circle. The method is based on a functional approach.