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About Sun's f95 with Interval Support
# Interval FAQ

Dominique Faudot -- What do X < Y and X > Y mean?

From Dominique Faudot
(faudot@u-bourgogne.fr):
## Interval arithmetic of functions?

I am just beginning with arithmetic of intervals applied to computer
graphics. I have a problem, which is the following:
Suppose we have f1(X) + f2(X), where f1 and f2 are functions, and X is an
interval.

- On which interval is f1+f2 defined? Is this interval (f1+f2)(X)?
- On which intervals are f'1(X), f'2(X), f'1+f'2, and (f1+f2)' defined?

Dominique Faudot

(rbk@usl.edu),
University of Southwestern Louisiana:
**On which interval is f1+f2 defined?**

f1 + f2 is generally defined where both f1 and f2 are, as with
real-valued functions.

**Is this interval (f1+f2)(X)?**

If f1 and f2 are evaluated, say, by evaluating each by replacing
the symbol X in the expression by intervals, then f1(X) + f2(X) will
contain the range of (f1+f2) over X, just as f1(X) contains the range
of f1 over X, and f2(X) contains the range of f2 over X. In that sense,
(f1+f2)(X) is always equivalent to f1(X) + f2(X). However, unlike
real-valued functions, different ways of writing down f1 and f2 that
are equivalent in real arithmetic give rise to different interval
values.

**On which intervals are f'1(X), f'2(X), f'1+f'2, and (f1+f2)' defined?**

Generally, these functions are defined generally where you can define
the corresponding real-valued functions. My explanation above for
the sum is also valid for the sum of the derivatives.

Think of interval values as BOUNDS ON THE RANGE that are not unique.

R. Baker Kearfott,
http://interval.louisiana.edu/kearfott.html

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About Sun's f95 with Interval Support
If *you* have a question related to validated computing, interval
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Last modified April 29, 1999.
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