Finding local maxima from interpolated function

[member 428835]

Hi PF!

I have data that I need to interpolate (don't want to go into details, but I HAVE to interpolate it). I'm trying to find the local maximas on a given domain. I've looked everywhere and still haven't been able to do it? Seems most people work with NDSolve, but I don't use that function.

Below is a simple code that illustrates my position. I'm trying to find the local maxima of $f$.

data = Transpose[{Table[i, {i, 1, 30}], RandomReal[{0, 1}, {1, 30}] // Flatten}];
ListLinePlot[data]
f = Interpolation[data];
Plot[{f[x]}, {x, 1, 10}]

 

[Dale]

Try

maxima = Table[FindMaximum[f[x], {x, i}], {i, 1, 9, .1}]
DeleteDuplicates[maxima,
Function[{a, b}, (Abs[a[[2, 1, 2]] - b[[2, 1, 2]]] < 0.1)]]

If you find that you are missing some maxima then you can always decrease the step size for your starting point.

 

[member 428835]

Thanks so much!