Algebraic Approach in the "Outer Problem" for Interval Linear Equations

Algebraic Approach in the "Outer Problem" for Interval Linear Equations The subject of our work is the classical "outer" problem for the interval linear algebraic System Ax = b with the square interval matrix A: find "outer" coordinate-wise estimates of the united solution set Σ formed by all solutions to the point systems Ax = b with A ∈ A and b ∈ b. The purpose of this work is to advance a new algebraic approach to the formulated problem, in which it reduces to solving one noninterval (point) equation in the Euclidean space of double dimension. We construct a specialized algorithm (subdifferential Newton method) that implements the new approach, then present results of the numerical tests with it. These results demonstrate that the proposed algebraic approach combines unique computational efficiency with high quality enclosures of the solution set. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Algebraic Approach in the "Outer Problem" for Interval Linear Equations

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 1997 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1009975421252
Publisher site
See Article on Publisher Site

Abstract

The subject of our work is the classical "outer" problem for the interval linear algebraic System Ax = b with the square interval matrix A: find "outer" coordinate-wise estimates of the united solution set Σ formed by all solutions to the point systems Ax = b with A ∈ A and b ∈ b. The purpose of this work is to advance a new algebraic approach to the formulated problem, in which it reduces to solving one noninterval (point) equation in the Euclidean space of double dimension. We construct a specialized algorithm (subdifferential Newton method) that implements the new approach, then present results of the numerical tests with it. These results demonstrate that the proposed algebraic approach combines unique computational efficiency with high quality enclosures of the solution set.

Journal

Reliable ComputingSpringer Journals

Published: Oct 14, 2004

References

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