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Cuchulainn
Posts: 20253
Joined: July 16th, 2004, 7:38 am
Location: 20, 000

Re: Mathematica high precision question

November 24th, 2019, 8:49 pm

I suppose Collector's [$]f(x)[$] is given/known a priori? e.g.  some polynomial or combination of math functions?
yes indeed (just a money making formula)
Right, the usual stuff.

Just one more thing; it is OLS
https://en.wikipedia.org/wiki/Least_squares

and not ODR

https://en.wikipedia.org/wiki/Deming_regression#Orthogonal_regression
 
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Cuchulainn
Posts: 20253
Joined: July 16th, 2004, 7:38 am
Location: 20, 000

Re: Mathematica high precision question

November 26th, 2019, 7:49 am

On a related remark, an alternative to the "usual suspects" (gradient/Hessian, derivative-free methods)+ many tweaks) is to optmiise using gradient flows (I have tested it on both OLS and ODR and ii is quite insensitive to random input). The underlying maths is more developed than GD:

https://camo.ici.ro/neculai/diff.pdf

I don;t know if MM supports Gradient Flows but I reckon NDSolve could be used. The only thing you need to know is the gradient.

https://forum.wilmott.com/viewtopic.php?f=34&t=101716