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MathGroup Archive 2010

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Help with Spline Interpolation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg113193] Help with Spline Interpolation
  • From: "Tim McShane" <tmcshane1 at verizon.net>
  • Date: Mon, 18 Oct 2010 05:46:51 -0400 (EDT)

Hi,
I am trying to interpolate 5 data points using spline curves in 
Mathematica using the Interpolation function.  I also want to specify 
the first derivative or slope of the spline curve at the end points 
only.  This is known as a "clamped" cubic spline.
I used the following code:

data1={{{2},3,-1},{{5},4,Automatic},{{9},6,Automatic},{{14},7,Automatic},{{20},5,1}}

data1Plot=Table[{data1[[i,1,1]],data1[[i,2]]},{i,1,Length[data1]}]

sfun=Interpolation[data1,Method->"Spline"]

grfx1=ListPlot[data1Plot,AxesOrigin=EF=82=AE{0,0}];
grfx2=Plot[sfun[x],{x,2,20}];
Show[grfx1,grfx2]

sfun'[2]
0.139481

sfun'[20]
-0.63457

This draws a smooth curve through the data points but does not reproduce 
the specified first derivatives at the end points.  The slope at the 
beginning and end points should be -1 and 1 respectively.  The 
interpolating function returned by Mathematica gives 0.139 and -0.635

Did I give the proper input parameters?  Please help.
Thank you,
Tim McShane



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