On the positivity of iterative methods

In this paper we study the positivity of some vector sequences produced by given vector-iteration. In our investigation we apply the wellknown power method (e.g. [5]). We give some sufficient conditions of the positivity of the gellerated vector sequence depending both on the initial vector and on the matrix of the iteration. Applying this result we formulate a sufficient condition of the power-positivity of a given quadratic matrix. Furthermore, we consider the numerical solu tion of the one dimensional heat conduction equation. Considering the results of [1] we give a condition that guaranties the positivity of the approximating vector sequence. Finally, we obtain some bounds for parameters of the discretization scheme. In the case of n = 2 we get a well-known sufficient condition, which was obtained by use of the Lorenz criterion ([4]).