MathGroup Archive 1999

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Complex Ratio Polynomial Fit

  • To: mathgroup at
  • Subject: [mg17256] Re: Complex Ratio Polynomial Fit
  • From: Jens-Peer Kuska <kuska at>
  • Date: Fri, 30 Apr 1999 02:34:42 -0400
  • Organization: Universitaet Leipzig
  • References: <7g0s0f$>
  • Sender: owner-wri-mathgroup at

Hi Colin,

Pade[] uses an analytic algorithm to construct a rational
approximation form a Taylor series expansion of  order K.
The Taylor expansion of the rational approximation has the same first
coefficients as the Taylor series as the Taylor series of the original.

The basic usage is to inlude the asymptotic behaviour of the function
into the approximation.

AFAIK the only rational approximation that can be obtained from discrete
data are Thiele's interpolation formula (25.2.50 in Abramowitz Stegun).
But this is an interpolation and not a approximation and the resulting
function satisfy the interpolation condition y[i]=f[x[i]].

I attach my Thiele.m package that will calculate a Thiele interpolation.

Hope that helps

Colin L C Fu wrote:
> Hiya,
> I was told that the add-on packages in Mathematica are useful to solve
> more complicated
> and particular problems.  Thanks!
> I tried to use Calculus'Pade' and Statistic'Nonlinear' to solve my
> initial problem.  i am nearly there.  The problems that I have when I
> used
> 1) Caluculus'Pade' is that the input has to be a function instead of
> data points.
> 2) Statistic'Nonlinear' is that I wouldnt be able to fit complex ratio
> polynomial in the form of  (a1*x^n + a2*x^(n-1) + ... + I * (b1*x^m +
> ... ) )/(c1*x^n + c2*x^(n-1))
> Please advise
> Regards
> Colin


(* Evaluation of a Thiele continued fraction for the data
   {x1,x2,..} and {y1,y2,..}.

   Author: J.-P. Kuska
   Last change: 10/14/93


Thiele::usage="Thiele[{x1,x2,..},{y1,y2,..},x] calculates a continued fraction due to
               Thiele, given the data {x1,x2..} (containing the x-values)
               and {y1,y2,..} (containing the y-values) Thiele calculates
               the resulting approximation f(x). The Pattern
               Thiele[{{xi,yi}..},x] is also supported."


    Module[{ data=Transpose[l],x,y},
            x=data[[1]]; y=data[[2]];
            For[i=1,i<=n, i++,
            For[i=1,i<n, i++,
            For[i=2, i<n, i++,
              For[j=1, j<=n-i, j++,
          ] /; Length[x]==Length[y]
End[ ]
EndPackage[ ]

  • Prev by Date: Re: infuriating Series[] question
  • Next by Date: Re: Question: getting list data into a matrix
  • Previous by thread: Complex Ratio Polynomial Fit
  • Next by thread: 3 bodies in Mathematica 3.0