FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2002, VOLUME 8, NUMBER 2, PAGES 567-610

S. P. Shary

Abstract

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The subject of our work is the classical ``outer'' problem for the
interval linear algebraic system
```$\mathbf Ax =
\mathbf b$ with the interval
matrix $\mathbf A$
and right-hand side vector $\mathbf b$ :
find ``outer''
coordinate-wise estimates of the solution set formed by all solutions
to the point systems $Ax = b$ with $A \in
\mathbf A$ and
$b \in \mathbf b$ .
The purpose of this work is to propose a new \emph{algebraic approach}
to the above problem, in which it reduces to solving one
\emph{point} (noninterval)
equation in the Euclidean space of the double dimension. We construct
a specialized algorithm (subdifferential Newton method)
that implements the new approach, present results of its numerical tests.
They demonstrate that the algebraic approach combines
exclusive computational efficacy with high quality enclosures
of the solution set.

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Last modified: November 26, 2002