Question

2. (a) Evaluate the function f (t) = .05sin(1000t)+.5cos(πt)−.4sin(10t) at the 101 points given by 0:.01:1. Plot the resulting broken line interpolant.

(b) In order to study the slow scale trend of this function, we wish to find a low degree polynomial (degree at most 6) that best approximates f in the least squares norm at the above 101 data points. By studying the figure from part (a) find out the smallest n that would offer a good fit in this sense. (Try to do this without further computing.)

(c) Find the best approximating polynomial v of degree n and plot it together with f . What are your observations?

Answer 1

data={{1., 5827.}, {3., 6242.}, {15., 6066.}, {60., 5972.}}

I want to get the interpolation line from ListPlot:

pl=ListPlot[data, Joined -> True,InterpolationOrder -> 2, PlotStyle -> Dashed, PlotRange -> {5900, 6300}]

8300 г 200 8100 6000 : 10 20 30 40 50

But I can't get the same dash line from InterPolation:

Plot[Interpolation[data, InterpolationOrder -> 2][x], {x, 1, 60}, 
     PlotStyle -> Dashed]

eeoot' 400' И4342 8200 8000F 10 20 40 80