How can I generate random sparse stable matrices ?
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I need to generate random matrices that are sparse and stable and control the sparsity level, I tried using matlab functions sprand and sprandn and use conditional "if" to check if the generated matrices have negative eigenvalues, but the generated matrices are often unstable and do not converge to the steady state.
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John D'Errico
2014-2-15
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There is simply no way that use of sprand or sprandn will yield matrices with all positive eigenvalues with any viable frequency.
However, you might use those tools to generate the random sparse matrices, then shift the eigenvalues. Gershgorin disks will suffice to know how much of a shift is necessary. The result may not be as purely "random" as you might want, but it very possibly is as good as you will get.
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