Thiele is a long story. From observing this demo, one can presume the data set
is of exponential decay ... yes it is. Exponential decay do not manouver on
long data set [water viscosity is expDecay 0.01 ... 100 °C , Thiele 0.01...critical]
Thiele fits as well SQRT look like data set ... etc.
Thiele from the web ... good luck !
Thiele does not come out of the Canada blue. Continued fractions origin from the
Mesopotamians. More recently, revived in the first IBM Main Frame, from which
the J_Fraction resulted [economized arithmetic operations]. Maple has conserved
the converter [hopefully till the end of the World].

On the other hand, PC's and more common computing machinery use rational fraction
for the approximation of the math functions ... name them, very many delivered
in Microsoft products, more from public lib's.

Carlos [are you there ?],
Please, complement with your "Automatic"
BTW, thanks for your valuable contribution in Smath Community.

Cheers to all ... Jean

Thiele_0 Demo.sm (57 KiB) downloaded 66 time(s).