# Optimal Enclosure of Quadratic Interval Functions

Optimal Enclosure of Quadratic Interval Functions In this paper, we analyze the problem of the optimal (narrowest) approximation (enclosure) of a quadratic interval function $$y(x_1 ,...,x_n ) = [y(x_1 ,...,x_n ) \bar y(x_1 ,...x_n )]$$ (i.e., an interval function for which both endpoint functions $$\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{y} (x_1 ,...,x_n ) {\text{and}} \bar y(x_1 ,...x_n )$$ , ..., x n) are quadratic) by a linear interval function. show that in general, this problem is computationally intractable (NP-hard). For a practically important 1D case (n = 1), we present an efficient algorithm. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Optimal Enclosure of Quadratic Interval Functions

, Volume 4 (4) – Oct 14, 2004
10 pages

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:1024415715798
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we analyze the problem of the optimal (narrowest) approximation (enclosure) of a quadratic interval function $$y(x_1 ,...,x_n ) = [y(x_1 ,...,x_n ) \bar y(x_1 ,...x_n )]$$ (i.e., an interval function for which both endpoint functions $$\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle-}}}{y} (x_1 ,...,x_n ) {\text{and}} \bar y(x_1 ,...x_n )$$ , ..., x n) are quadratic) by a linear interval function. show that in general, this problem is computationally intractable (NP-hard). For a practically important 1D case (n = 1), we present an efficient algorithm.

### Journal

Reliable ComputingSpringer Journals

Published: Oct 14, 2004

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