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