Convergence of skew-symmetric iterative methods

We propose a new technique for studying the convergence of triangular skew-symmetric and product triangular skew-symmetric iterative methods (introduced earlier by the first author) based on the notion of a field of values of a matrix. We obtain formulas connecting the field of values of the initial matrix, that of the matrix which determines the iterative method, and eigenvalues of the iterative matrix. We prove that the mentioned methods can converge even if the initial matrix is not dissipative.