Re: Help with Spline Interpolation

*To*: mathgroup at smc.vnet.net*Subject*: [mg113244] Re: Help with Spline Interpolation*From*: "Tim McShane" <tmcshane1 at verizon.net>*Date*: Wed, 20 Oct 2010 04:08:31 -0400 (EDT)

Thank you Chris for your good suggestion. I added an extra point on either end to match the specified 1st derivatives. This did result in a curve with slopes much closer to -1 and 1 at the end points (-0.512 and +0.634). However, I was looking for an exact mathematical boundary condition for the 1st derivatives at the end points of the cubic spline curve. There is a Mathematica algorithm for doing this written by Joseph M. Herrmann available on the Wolfram Library Archive. I wanted to see if I could do the same thing by using the built-in Mathematica Interpolation function. Thanks, Tim McShane ----- Original Message ----- From: "Christopher Arthur" <aarthur at tx.rr.com> To: <mathgroup at smc.vnet.net> Sent: Tuesday, October 19, 2010 5:56 AM Subject: [mg113244] [mg113223] Re: Help with Spline Interpolation > Hi Tim, > > As an experiment, try to put a point on either side of the bounds so > that the spline isn't terminating at 2 and 20 but flows through it...see > if the derivatives are better then. Perhaps the endpoints are not > differentiable in the model, and that is why the problem is. > Christopher Arthur > > Tim McShane a =E9crit : >> 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 >>