Optimization of parameters of stationary models in a unitary space

Presented in the paper is a variational method of optimizing the coefficients of a vector difference equation with constant (matrix) complex coefficients, which approximates by one of its solution a prescribed finite sequence of complex vector equidistant counts. It is shown that an appropriate variational problem with unfastened boundaries is equivalent to the discovery of a chain of subspaces, which is generated by a polynomial in an isometric operator in an abstract Hilbert space. The chain is such that it is remote to a maximum from an arbiitrarily specified element of this space. To afford an effective recursion solution of the problem, use is made of counter processes of orthogonalization and special iterative procedures of optimizing the parameters of an equation that approximates the process under study in a finite observation interval.