Re: Interpolation and plot doing strange things with mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg88978] Re: Interpolation and plot doing strange things with mathematica*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Thu, 22 May 2008 06:16:59 -0400 (EDT)*Organization*: Uni Leipzig*References*: <g134je$m3l$1@smc.vnet.net>*Reply-to*: kuska at informatik.uni-leipzig.de

Hi, if you make a approximation based on a Fourier series it converges "in the middle" and never point wise The most famous example is the Gibbs phenomenon. http://en.wikipedia.org/wiki/Gibbs_phenomenon Regards Jens ratullochjk2 at gmail.com wrote: > Greetings All > > I run these commands that I've had plenty of help getting to > work...but the plot doesn't follow the points, as you can see in the > plot. At the end it just goes crazy and when I test the points with > > input s[0] > output is -3.73293 > why are the numbers so out of sync... at s[0] it should be -2 not > -3.73293 > > I try increasing the number in the line > N[FourierTrigSeries[f[x], x, 25, FourierParameters -> {-1, 1/138}]] > (I've changed the number 25 to over 100 and the problem seems to get > worse) > > See code below: > > In[89]:= data3 = {{0, -2}, {7, 1}, {10, 6}, {12, -2}, {18, -6}, {27, > 6}, {34, > 4}, {42, -6}, {49, -5}, {56, 4}, {62, 3}, {67, -5}, {70, -3}, {79, > 3}, {83, 7}, {88, -3}, {89, -8}, {96, 7}, {105, > 9}, {113, -8}, {122, -9}, {131, 9}, {132, > 1}, {134, -9}, {138, -2}}; > f = Interpolation[data3, PeriodicInterpolation -> True]; > > << "FourierSeries`" > > s[x_] = N[ > FourierTrigSeries[f[x], x, 25, FourierParameters -> {-1, 1/138}]] > > discr = Interpolation[data3 /. {x_, y_} -> {x, y}, > InterpolationOrder -> 1]; > > g[x_] = Piecewise[{{discr[x], 0 < x < 138}, {0, True}}]; > > Show[Plot[s[x], {x, 0, 138}, PlotStyle -> Red, > PlotRange -> {-15, 15}], Plot[g[x], {x, 0, 138}, Filling -> Axis], > ListPlot[data3, Filling -> Axis, PlotRange -> {0, 138}]] > > tia sal2 >