Özet:
The modified stationary iterative methods of the solution of system of the linear algebraic equations (SLAE) are considered.For SLAE with a three-diagonal matrix with constant factors it is shown, that eigenvalues of modified matrices or the operator, participating in series of simple iteration, are expressed through roots of Chebyshev polynomials of the second kind. On this basis strict expressions through factors of an initial matrix for optimum parameter of convergence and spectral radius are found. So for Successive Overrelaxation method strict expression for the optimum parameter of convergence w0 laying on an interval (0,2) is found. It is shown, that convergence of the optimum modified series essentially improves.
