3.146 FAQ-884 How to get a good fit with a very large or a very small parameter?

goodfit-for-large-small-param

Last Update: 9/21/2017

When you do curve fitting, you might meet these problems:

Origin returns missing value in standard errors when you perform fitting with a large parameter.
Fit can not converge when you perform fitting with a very small parameter.

In both cases, we need to redefine the equations to avoid a very large or a very small parameter. For example:

$y = A \cdot x$ ; if A is a large parameter, we can redefine the equation as $y=(A' \cdot 1E3) \cdot x$ . After fitting, we can get $A = A'\cdot 1E3$ ;
$y = A \cdot x$ ; if A is a small parameter, we can redefine the equation as $y=(A' \cdot 1E-3) \cdot x$ . After fitting, we can get $A = A' \cdot 1E-3$ ;

Another actual example is the nonlinear implicit diode function:

$f = Is \cdot {e^{(\frac{{V - I \cdot Rs}}{{k \cdot T}} - 1)}} + \frac{{V - I \cdot Rs}}{{Rsh}} - I\,\!$ , k is in $eV{K^{ - 1}}\,\!$ as a unit.

To do fitting with this function, firstly, we can reset the parameter $Is$ to $I's$ , where $I's=Is*exp(-20)$ , then the parameter $I's$ won't be too small.