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.