Brian,

Jonathan, Jerry, et al
As to the number of potential observations. Thousands of series, 10s to hundreds of thousands of observations per series at a minimum. Possibly millions. So computational efficiency isn't a luxury, it is a requirement.
Brian

The following method is fairly efficient. The process, on my slow Mac Mini, take 2 seconds to process one million data points.

on mouseUp
   put .1 into tAngle
   --Create one million data points
   repeat 1000000 times
      put sin(tAngle*pi/180) & cr after tempList
      add 5 to tAngle
   end repeat
   --Now find the minima and maxima
   put the sec into tStartTime
   put MinMax(tempList) into field 1
   put the sec - tStartTime into msg box
   beep
end mouseUp

function MinMax tList
   put line 1 of tList into yOld
   put 0 into dyOld
   repeat for each line yNew in tList
      put yNew - yOld into dy
      put dy * dyOld into tChange
      if tChange  < 0 or tChange = 0 then
         put yNew & cr after tExreema
      end if
      put ynew into yOld
      put dy into dyOld
   end repeat
   return tExreema
end MinMax


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