CS 6391
Interval Computations

What is interval computations?

• You think computers are too smart?
Sometimes they are, but often, they are silly.
• You give them the number, they think it is exact.
• If you give a computer your height in centimeters, and ask to translate it into inches,
the computer will give you 13 digits after the decimal points.
• Do these digits make sense? Of course, not: no one is exactly 170 cm tall.
• For this simple formula, it is easy to tell how many digits make sense.
• However, for complex data processing algorithms, this is not so easy (it is actually NP-hard).
• This inaccuracy may not be critical for measuring height.
• However, it is definitely critical when you are computing the trajectory of a manned space flight:
there, a computational inaccuracy can be catastrophic.
What you will learn in this class:
• You will learn how input uncertainties influence the computation results.
• You will learn about the applications:
• to manufacturing,
• to robotics,
• to geoinformatics (processing geophysical data),
• to bioinformatics (processing bioinformatics data),
• to economics,
• to computer graphics,
• to computer security and privacy
(where intervals are introduced on purpose, to avoid disclosing exact values).
You will also:
• have a chance to work on the uncertainty aspects of your thesis or dissertation research,
• or, if you are interested, pick up a topic of your own related to uncertainty!
But will it be mathematically intimidating?
Especially for those students who might have previously struggled with some math concepts?
• not really;
• the only math skills that we will assume is
the ability to compute the derivatives
(and thus, to find maxima and minima);
• if you do not remember the corresponding formulas by heart,
it is OK, we will go over them again;
• during the course, we will also learn a little bit: