An interval extension based on occurrence grouping
In interval arithmetics, special care has been brought to the definition of interval extension functions that compute narrow interval images. In particular, when a function f is monotonic w.r.t. a variable in a given domain, it is well-known that the monotonicity-based interval extension of f comput...
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| Published in: | Computing 2012-03, Vol.94 (2-4), p.173-188 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | eng |
| Subjects: | |
| Online Access: | Get full text |
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| Summary: | In interval arithmetics, special care has been brought to the definition of interval extension functions that compute narrow interval images. In particular, when a function
f
is monotonic w.r.t. a variable in a given domain, it is well-known that the monotonicity-based interval extension of
f
computes a sharper image than the natural interval extension does. This paper presents a so-called “occurrence grouping” interval extension [
f
]
og
of a function
f
. When
f
is
not
monotonic w.r.t. a variable
x
in a given domain, we try to transform
f
into a new function
f
og
that is monotonic w.r.t. two subsets
x
a
and
x
b
of the occurrences of
x
:
f
og
is increasing w.r.t.
x
a
and decreasing w.r.t.
x
b
. [
f
]
og
is the interval extension by monotonicity of
f
og
and produces a sharper interval image than the natural extension does. For finding a good occurrence grouping, we propose a linear program and an algorithm that minimize a Taylor-based over-estimate of the image diameter of [
f
]
og
. Experiments show the benefits of this new interval extension for solving systems of nonlinear equations. |
|---|---|
| ISSN: | 0010-485X 1436-5057 |