If I have two independent variables x,y, and two measurements, m1, m2 with errors. And the dependence is thus:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

m_1 \pm \delta m_1 = f[x,y]

[/tex]

[tex]

m_2 \pm \delta m_2 = g[x,y]

[/tex]

Now in my case, f and g are complicated expressions of x and y with no simple solution. (Actually I think i can solve one for x, but not for y).

Now if the equations were easy, I could solve for x and y:

[tex]

x \pm \delta_x = F[m_1, m_2,...]

[/tex]

[tex]

y \pm \delta_y = G[m_1, m_2,...]

[/tex]

And from there add the errors in quadrature to get the x and y errors.

BUT if I cant solve for x and y independently, and I must use numerical solutions to get the results ( I can, its easy). How can I go about getting the ERRORS? Is there another way I can solve for the errors and numerically solve for them, or a different method?

I have Mathematica if that helps.

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# Error propagation with two functions, two unknowns.

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