Classification of solutions to systems of two-sided equations with interval coefficients. (English) Zbl 1154.65036

A system \(f({\mathbf A}, x)= g({\mathbf B}, y)\) of two-sided equations with interval coefficients is a set of systems of equations \(f(A, x)= g(B, y)\) for unknown vectors \(x\in X\subseteq\mathbb{R}^k\), where \(A\in\mathbb{R}^{m\times n}\), \(B\in\mathbb{R}^{m\times k}\) are elements of given interval matrices \({\mathbf A}= [\underline A,\overline A]\), and \({\mathbf B}= [\underline B,\overline B]\) respectively, and where \(f:{\mathbf A}\times X\to\mathbb{R}^m\), \(g: {\mathbf B}\times Y\to\mathbb{R}^m\) are given functions. The paper motivates such interval equations and introduces weak solutions, (left/right/-)tolerance solutions and (left/right/-)strong solutions. Moreover, it formulates and proves equivalent criteria for them, and relations between them. Several examples illustrate the theory.


65H10 Numerical computation of solutions to systems of equations
65G30 Interval and finite arithmetic