Introduction
The main focus in the interval arithmetic is on the simplest way to calculate upper and lower endpoints for the range of values of a function in one or more variables. These barriers are not necessarily the supremum or infimum, since the precise calculation of those values can be difficult or impossible; it can be shown that that task is in general NP-hard.
Treatment is typically limited to real intervals, so quantities of form
where and are allowed; with one of them infinite we would have an unbounded interval, while with both infinite we would have the extended real number line.
As with traditional calculations with real numbers, simple arithmetic operations and functions on elementary intervals must first be defined. More complicated functions can be calculated from these basic elements.
Read more about this topic: Interval Arithmetic
Famous quotes containing the word introduction:
“Such is oftenest the young man’s introduction to the forest, and the most original part of himself. He goes thither at first as a hunter and fisher, until at last, if he has the seeds of a better life in him, he distinguishes his proper objects, as a poet or naturalist it may be, and leaves the gun and fish-pole behind. The mass of men are still and always young in this respect.”
—Henry David Thoreau (1817–1862)
“For the introduction of a new kind of music must be shunned as imperiling the whole state; since styles of music are never disturbed without affecting the most important political institutions.”
—Plato (c. 427–347 B.C.)
“We used chamber-pots a good deal.... My mother ... loved to repeat: “When did the queen reign over China?” This whimsical and harmless scatological pun was my first introduction to the wonderful world of verbal transformations, and also a first perception that a joke need not be funny to give pleasure.”
—Angela Carter (1940–1992)