# Algorithm used by Fit[]

Does anyone know what algorithm Mathematica's basic Fit[] function uses? Is it proprietary?

I'm trying to do some pretty basic, linear, polynomial data fitting (albeit with poly degrees of about 15) in IDL but I'm finding that Mathematica's Fit[] function does a better job, and fails less often, than any of IDL's routines. So I was hoping to find out which algorithm Fit[] is using and translate it into IDL.

And for the record, if I use FindFit[..., Method->Automatic] it gives the same results as Fit[]. In another thread it was stated that FindFit[] defaults to the SVD algorithm if no Method is specified, so I wonder if this is the algorithm used by Fit[] as well (or perhaps just a matrix inversion).

Much appreciated.

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• – J. M. is away Mar 8 '16 at 23:22
• Almost certainly using SVD as @J.M. notes. For fitting degree 15 polynomials though you might want to consider a basis other than the standard one (1,x,x^2,...) to get better numeric stability. – Daniel Lichtblau Mar 8 '16 at 23:30
• J. M. and Daniel, thanks. Daniel, maybe Legendre Polynomials? Interesting that IDL's svdfit() function and Mathematica's Fit[] function give very different results using SVD. I suppose the devil is in the details. – Adam Mar 9 '16 at 0:23
• You could consider using Gram polynomials if your abscissas are equispaced; otherwise, the Chebyshev or Legendre basis can be used. – J. M. is away Mar 9 '16 at 0:54