[Maxima] Problem with expand in lagrange interpolation
fateman at cs.berkeley.edu
Wed Jun 13 14:33:19 CDT 2007
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu
> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of Daniel Lakeland
> Sent: Wednesday, June 13, 2007 11:02 AM
> To: maxima at math.utexas.edu
> Subject: Re: [Maxima] Problem with expand in lagrange interpolation
> By expanding a high degree polynomial we typically create a
> numerically unstable result, since the first term begins to dominate
> rapidly, among other things.
> The newton divided difference formula is designed to avoid that, I
> think it's the same thing as the horner scheme that we get from
> "horner" in maxima
> so perhaps instead of "expand" try applying "horner"
Sorry, no. A divided difference interpolation form is not the same as
Also the wikipedia entry for Horner is poor. It includes the falsehood...
"Minimizing the number of multiplications is desirable because they are time
consuming and numerically unstable compared to addition."
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