1998 , Volume 3, № 2, p.67-114

The subject of our work is the classical ``outer`` problem for the interval linear algebraic system Ax = b with the interval [Java Applet]-matrix A and interval right-hand side n-vector b: find ``outer`` component-wise estimates of the solution set formed by all solutions to the point systems Ax = b with A$\in$A and b $\in$b, that is, evaluate $\min\{\,x_k \mid x\in\Sigma\,\}$ from below and $\max\{\,x_k \mid x\in\Sigma\,\}$ from above, $k = 1,2, \ldots, n$. The purpose of this work is to advance a new algebraic approach to the problem, in which it reduces to computing the algebraic solution to an auxiliary system in Kaucher complete interval arithmetic, or, what is equivalent, to solving one noninterval (point) equation in the Euclidean space of the double dimension R²ⁿ. We construct a specialized algorithm - subdifferential Newton method - that implements the new approach, present results of numerical testing that demonstrate its exclusive computational efficacy with high quality enclosures of the solution set.

*65F30 Other matrix algorithms

65G30 Interval and finite arithmetic

*G.1.0 General (Numerical Analysis)

G.1.3 Numerical Linear Algebra