These 4 examples illustrate advanced use of Polyfit
of which, the core solver is Cholesky LS [Least Squares].
Lot of utilities as needed for else project(s).
linfitCheby transits coefficients via file.
As given it should create in your system, if not: report.

Jean

Poly 0 Read First Edu.sm (36 KiB) downloaded 76 time(s).
Polynomial fit Methods [linfitCheby].sm (43 KiB) downloaded 75 time(s).
Polynomial fit Methods [ Rational Iterate 'J'].sm (54 KiB) downloaded 62 time(s).
Genfit NonLinearFit [Revisit].sm (88 KiB) downloaded 76 time(s).

Wrote

These 4 examples illustrate advanced use of Polyfit

... next advanced fitting session is Thiele Continued Fraction.
It fits many type of shapes, the most remarkable ones are
of type hyperbolic. They may be the unique interpolation fitter
like many of ISA [International Standard Atmosphere].
Their reduced form J(β,x) origin from the first Main Frames
before the rational fractions [Padé] were available.
Continued Fractions are believed rediscovered from stone sculptures
from Mesopotamians 4000 BC ... God was not yet dead.
I got initiated to CF from F.B. Hildebrand.

Polynomial fit Methods [Thiele Cfr(K,X,x)].sm (76 KiB) downloaded 76 time(s).