# Cheap and Tight Bounds on the Solution Set of Perturbed Systems of Nonlinear Equations

Cheap and Tight Bounds on the Solution Set of Perturbed Systems of Nonlinear Equations This paper presents an iterative method for computing an outer interval bound on the solution set of parameters-dependent systems of non-linear equations for the case where the parameters take on their values within present intervals. The method is based on a recently suggested alternative linear interval enclosure of factorable non-linear functions in a given box. It comprises two stages: during the first stage, a relatively narrow starting box is determined using an appropriate inflation technique while the second stage aims at reducing the width of the starting box. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Cheap and Tight Bounds on the Solution Set of Perturbed Systems of Nonlinear Equations

, Volume 7 (5) – Oct 3, 2004
10 pages

/lp/springer_journal/cheap-and-tight-bounds-on-the-solution-set-of-perturbed-systems-of-nICAk603Cx
Publisher
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:1011475926711
Publisher site
See Article on Publisher Site

### Abstract

This paper presents an iterative method for computing an outer interval bound on the solution set of parameters-dependent systems of non-linear equations for the case where the parameters take on their values within present intervals. The method is based on a recently suggested alternative linear interval enclosure of factorable non-linear functions in a given box. It comprises two stages: during the first stage, a relatively narrow starting box is determined using an appropriate inflation technique while the second stage aims at reducing the width of the starting box.

### Journal

Reliable ComputingSpringer Journals

Published: Oct 3, 2004

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