Interval arithmetic - SciPy Conferences

Functions of intervals (2)
R ∪ {−∞, +∞}. Let f([a, b]) be the image of the bounded interval, equation
closed interval [a, b] under the function f. Real analysis
result.
teaches that if the interval is bounded and the The lattice generated by t
function is continuous over the interval, then f([a, b]) y real set, L(IR ∗ ), is the sm
is also a closed, bounded interval, and, more significantly,
2 ing IR ∗ that is closed und
this extension accomodate
[
]
the union of two intervals
f([a, b]) = min f(x), max (1) in the lattice can always b
x∈[a,b] x∈[a,b]
of closed intervals in R ∗ . I
Computing the minumum and maximum is trivial if
the function is monotonic (Figure 1), and −1/4 also for
the non-monotonic standard mathematical functions 0
>>> k = interval([0, x 1]
represents the the union [0
The intervals 2 [0, 1], [2, 3],
(even-exponent power, cosh, sin, cos...) these are relatively
easy to determine.
connected components of k
sists of only one componen
>>> interval[1, 2]
interval([1.0, 2.0])
signifying the interval 8[1, 2