Systems of linear equations inside given intervals

Milan Hladík

Abstract

We consider a system of linear equations $Ax=b$, where entries of $A$ and $b$ varies inside given intervals. In traditional interval analysis, all parameters are supposed to vary simultaneously and independently. However, in real-life problems, dependences between parameters is a common phenomenon. Including such dependences into interval computations is a big challenge. We show several kinds of the most frequent dependences and present solution set characterization by means of nonlinear inequalities.