minima and maxima

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.