Method of reduction for interval system of linear algebraic equations and its application to modeling a small hydroelectric power station

Estimation Method for a Set of Solutions to Interval System of Linear Algebraic Equations with Optimized “Saturated Block” Selection Procedure

“…Papers [11][12][13] propose the minimization of maximal prediction error in the range of values of input variables x χ ∈ r as the criterion of selecting the optimal "saturated block": If all the equations in ISLAE (4) are numbered: 1,...,i,...,N, respectively, then each equation in the "saturated block" has a unique number n j , where n is number of the equation from system (4), j=1,...,m is its index number in the "saturated block". Then expression (10) can be rewritten as:…”

“…Let us choose a "saturated block" from ISLAE randomly, calculate its solution area and build the corridor of prediction by interval models: It should be noted that procedure (14) is simple as it is implemented for the finite set of points ,1,..., Papers [11][12][13] prove that if the vector max…”

“…As known from [1][2][3], on the one hand there may be equations in ISLAE that do not define the solution area, and on the other hand there may be interval equations that do not change significantly the configuration and size of the solution area. One of such methods is described in papers [11][12][13]. It consists in defining a solution area configuration at the initial stage.…”