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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.

MSC:

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