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In Matlab, I need to create a symmetric matrix with a given sparsity pattern and whose condition number is low ($\leq 10$). The matrix is sparse (more than half of its entries are zero).

From what I already know, generally if diagonal entries are larger and if the value of the entries are taken from a function, the condition number will be low.


Update

As an example of structure, we can consider Jacobian matrices or matrices whose graph is a star.

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  • $\begingroup$ The identity matrix fullfills your conditions. You need to be more precise. $\endgroup$ – nicomezi Aug 14 '18 at 6:35
  • $\begingroup$ @nicomezi it has not the specified structure. $\endgroup$ – M a m a D Aug 14 '18 at 6:36
  • $\begingroup$ Well, more then half of the entries are zero, diagonal entries are larger then nondiagonal and those are taken by the null function. That is why I am asking you to be more precise. $\endgroup$ – nicomezi Aug 14 '18 at 6:38
  • $\begingroup$ @nicomezi I updated the question $\endgroup$ – M a m a D Aug 14 '18 at 6:40
  • $\begingroup$ @RodrigodeAzevedo the value of non-zero entries are random (random for top triangle, the same will be used for bottom triangle) $\endgroup$ – M a m a D Aug 15 '18 at 10:08
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Is there a reason you are not using sprandsym(n,density,rc) with density$\geq 0.5$ and rc$\in (0.1,\infty)$ (documentation)?

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  • $\begingroup$ I don't know what that is!!! $\endgroup$ – M a m a D Aug 15 '18 at 10:07

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