FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

**Algebraic approach in the "outer problem" for interval linear systems**

S. P. Shary

Abstract

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The subject of our work is the classical "outer" problem for the
interval linear algebraic system $$**A**x
= **b** with the interval
matrix $$**A**
and right-hand side vector $$**b**: find "outer"
coordinate-wise estimates of the solution set formed by all solutions
to the point systems $Ax=b$ with $A$Î
**A** and
$b$Î
**b**.
The purpose of this work is to propose a new *algebraic
approach* to the above problem, in which it reduces to solving one
*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.

All articles are
published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k02/k022/k02213h.htm

Last modified: November 26, 2002