Re: Re: Fit or Interpolate

*To*: mathgroup at smc.vnet.net*Subject*: [mg39245] Re: [mg39231] Re: Fit or Interpolate*From*: Dr Bob <drbob at bigfoot.com>*Date*: Wed, 5 Feb 2003 00:11:53 -0500 (EST)*References*: <200302040723.CAA24653@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Interpolation[data][x] is perfectly good syntax. For instance: data = {#, #^3 + Random[]} & /@ Range[0, 5, 0.2]; x=3; Interpolation[data][x] 27.9333 Bobby On Tue, 4 Feb 2003 02:23:45 -0500 (EST), Bill Rowe <listuser at earthlink.net> wrote: > On 2/3/03 at 1:10 AM, sophtwarez at hotmail.com (David Seruyange) wrote: > >> What is the difference between using Fit and Interpolation? >> f[x_]=Fit[data, {1,x},x] -or-f[x_]=Interpolation[data][x] > > There are several differences between the expressions above > > First, Interpolation[data][x] isn't correct syntax. It should be > Interpolation[data]. Interpolation returns a pure function of data. By > default that is a 3rd order polynominal that passes through each of the > points specified by the variable data. > > In contrast, Fit[data,{1,x},x] returns a best fit *line* for the points > specified by data. The result is not a pure function but an expression. > The result is a least squares fit to the data and will not pass through > the points specified unless they lie exactly on a line. > > The two functions, Interpolation and Fit, are intended for different > purposes. > > Suppose you had a list of data points that were known to be accurate to > the precesion specified and wanted to estimate the value of the unknown > function at an intermediate point. For this you would use interpolation > since you want the result to pass through each of the data points you > started with. > > Now suppose you had a list of data points where each data point you have > is really the sum of a true value and a random error. The best result > would ideally subtract out the error and yeild the true values. So, you > would definitely not want the result to pass through the points with > error. For this problem you would use Fit. > > -- majort at cox-internet.com Bobby R. Treat

**References**:**Re: Fit or Interpolate***From:*Bill Rowe <listuser@earthlink.net>