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I have a matrix, with entries are series with numerical coefficients

$$ \begin{pmatrix} G(q) & F(q) \\ F(q) & G(q\rightarrow-q) \end{pmatrix} $$

With $G(q)$ is an expansion obtained with NIntegrate like:

G(q)=0.0335759 + 0.0133953 q^2 - 
 0.00185145 q^4 - (0. + 0.0293107 I) \[CapitalOmega] + (0. + 
    1.40567 I) q^2 \[CapitalOmega] - 41499.1 \[CapitalOmega]^2 + (
 0.010601 \[CapitalOmega]^2)/q^2 + ((0. + 
    5.68222 I) \[CapitalOmega]^3)/q^2 - (
 6225.96 \[CapitalOmega]^4)/q^4

Then I solve the determinant equals 0 and found $\Omega$ in terms of $q$, more precisely the proportionality coefficient c; $\Omega=c q$.

The problem is that if I add more digits, so WorkingPrecision->20 and solve again, I got a totally different result; it even changes from real to imaginary and the value is different.

Is it always more precise to add more working precision? does anyone know how to add the uncertainty and work with number of the form: $ x \pm dx$?

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  • $\begingroup$ Welcome to Mathematica.SE! I suggest that: 1) You take the introductory Tour now! 2) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! 3) As you receive help, try to give it too, by answering questions in your area of expertise. $\endgroup$ Commented Jul 21 at 12:52
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    $\begingroup$ The best is to show the full code of your example so others can follow it (and help). Eventually try to find a minimal working (or not) example that people can use to test. $\endgroup$ Commented Jul 21 at 12:53
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    $\begingroup$ Since you don't specify the precision of your constants (e.g. "0.335759"), Mathematica will assume that they are only accurate to Machine Precision, which is less that 20 decimal places. Intermediate results will have variable precision. I can't explain what you see, but I would try increasing the precision of your coefficients (if you can). $\endgroup$ Commented Jul 21 at 20:22
  • $\begingroup$ I can add more digits, because each coefficient are obtained by numerical integration. But I can't find an option within NIntegrate that would print the result and error estimate $\endgroup$ Commented Jul 22 at 20:57

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