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Determinants method of explanatory variables set selection to linear model

Rzymowski W., Surowiec A.

Advances in Science and Technology. Research Journal

2014

Vol. 8, nr 23

80--87

The determinants method of explanatory variables set selection to the linear model is shown in this article. This method is very useful to find such a set of variables which satisfy small relative error of the linear model as well as small relative error of parameters estimation of this model. Knowledge of the values of the parameters of this model is not necessary. An example of the use of the determinants method for world’s population model is also shown in this article. This method was tested for 224 – 1 models for a set of 23 potential explanatory variables. 5 world’s population models with one, two, three, four and five explanatory variables were chosen and analysed.

On positive reachability of time-variant linear systems on time scales

Bartosiewicz Z.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2013

Vol. 61, nr 4

905--910

Positive reachability of time-variant linear positive systems on arbitrary time scales is studied. It is shown that the system is positively reachable if and only if a modified Gram matrix corresponding to the system is monomial. The general criterion is then specified for particular cases of continuous-time systems and various classes of discrete-time systems. It is shown that in the case of continuous-time systems with analytic coefficients the conditions for positive reachability are very restrictive, similarly as for time-invariant systems.