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Re: Interpolation: Method->"Spline"

  • To: mathgroup at smc.vnet.net
  • Subject: [mg98245] Re: Interpolation: Method->"Spline"
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Fri, 3 Apr 2009 04:38:34 -0500 (EST)

On 4/2/09 at 4:46 AM, dh at metrohm.com (dh) wrote:

>does anybody know what sort of splines Wolfram choose to implement.
>One would assume that normal splines are the thing to do, but the second
>derivative is not zero at the ends as the following shows:

>d = Table[RandomReal[{-1, 1}], {5}]

>f = Interpolation[d, Method -> "Spline"];

>Plot[f[x], {x, 1, Length[d]},

>Epilog -> Point[Transpose[{Range[Length[d]], d}]]]

>Plot[f'[x], {x, 1, Length[d]}]

>Plot[f''[x], {x, 1, Length[d]}]

When you do FullForm[Interpolation[d,Method->"Spline"] you will
see part of the structure of f is a BSplineFunction. This leads
me to believe the spline basis is a B-spline. And since the
documentation for BSplineFunction states the default is a cubic
B-spline, I assume specifying Method->"Spline" results in a
cubic B-spline interpolation.



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