The plural of
minimum and
maximum respectively, these terms come into play in both
mathematics and
computational analysis where a minimum or maximum may only apply in some
neighbourhood of the data set's
range.
For example, the function y=sin x, the sin wave, has a minimum every 180 degrees, starting at x=270 degrees, and a maximum every 180 degrees, starting at x=90. This can be seen from the graph of the sin wave which looks like this:
|
| _ _
|/ \ / \ \ x=1 (at top of line)
...--+---\---/---\--...
_/| \_/ \_
| \ x=-1 (at top of line)
^ ^ ^ ^ ^
9 2 4 6
0 0 7 5 3
0 0 0
degrees
In this example, the
local minimum and the
global minimum are equal (as are the global and local maximum), but in many other cases, most notably in
non-linear functions, minima and maxima can differ and finding the
global minimum can be a
hard problem.