Re: Mathematica "Interpolation" function

*To*: mathgroup at smc.vnet.net*Subject*: [mg72015] Re: Mathematica "Interpolation" function*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Fri, 8 Dec 2006 06:18:05 -0500 (EST)*Organization*: The University of Western Australia*References*: <ek98a7$jpi$1@smc.vnet.net>

In article <ek98a7$jpi$1 at smc.vnet.net>, Lorents <lorenzo at amp.fi> wrote: > I'm trying to understand how mathematica produces interpolations in 1D > with the "Interpolation" command. I understood it uses piecewise > polynomial of the degree specified by InterpolationOrder. > As far as I understand this method never produces truly smooth functions > as nothing is done to elimitate the jump discontinuities in the > derivatives of the joined polynomials. Yes -- but note that if you know any derivatives you can pass them to Interpolation. From the online help: Data can be given in the form {{x1, {f1, df1, ddf1, ...}, ...} to specify derivatives as well as values of the function at the points xi. You can specify different numbers of derivatives at different points. Cheers, Paul _______________________________________________________________________ Paul Abbott Phone: 61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) AUSTRALIA http://physics.uwa.edu.au/~paul