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. ). 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  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 ().
|Tijdschrift||Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös nominatae. Sectio computatorica|
|Status||Gepubliceerd - 2000|