Re: Error propagation through a iterative root-finding function

On Apr 23, 12:08 pm, spellu...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
(Peter Spellucci) wrote:
In article <f2644e07-3736-4497-a8ed-ba1858a41...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
 Yevgen Barsukov <evgen...@xxxxxxxxx> writes:

Here is a problem that might have an obvious solution, please
enlighten me.

I have a function f(x, P) that can not be expressed analytically (say
it includes linterly interpolation of data), where parameters in array
P have standard deviations associated with them.

I need to find x that satisfies y = f(x,P), so I am using iterative
root function to do it,
e.g. x = root(f(x,P) - y, x)

How can I found the standard deviation of x, if I know standard
deviations of parameters P and x?
Is there any numerical method to do it for arbitrary function f?

Regards,
Yevgen

if f depends linearly on P then you will get a linear transformation
of the original distribution, depeding on x. otherwise things can be become
quite complicated. better ask the question in the statistics group.
what I as a nonstatistician would do: draw a lot of values of P
from its distribution and build the empirical distribution function
of f(x,P) for a grid of  x values and fit expectation and variance
as functions of x.
further decisions based on these.
(experimental error analysis)

hth
peter

Thanks Peter.
Yes, function can be assumed linear in the vicinity of x.
Unfortunately I can not do a "wide swap" approach in this case,
as it is embedded application and resources are limited.

Regards,
Yevgen
.

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